Wireless power supply system and power receiver

ABSTRACT

A wireless power supply system includes a power transmitter having a power-transmitting coil to which AC power of a frequency is input from a power source; and a power receiver having a power-receiving coil magnetically coupled to the power-transmitting coil at a coupling coefficient, and a first power-receiving-side series element coupled in series to the power-receiving coil and having imaginary impedance, in which the frequency, the coupling coefficient and the imaginary impedance are determined on the basis of satisfying a predetermined relationship.

This application is a Continuation application based on InternationalApplication No. PCT/JP2016/071825, filed Jul. 26, 2016, which claimspriority on Japanese Patent Application No. 2015-169841, filed Aug. 28,2015, the contents of which are incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to a wireless power supply system and apower receiver.

BACKGROUND

In recent years, there have been known wireless power supply systemsthat supply electric power using electromagnetic induction, magneticfield resonance or the like from a power transmitter including apower-transmitting coil to a power receiver including a power-receivingcoil. In such systems, magnetic flux generated by the power-transmittingcoil is interlinked with the power-receiving coil, whereby electricpower is transmitted between the coils. For this reason, the efficiencyof power transmission (transmission efficiency) is influenced by apositional relationship between the power-transmitting coil and thepower-receiving coil.

The battery charging of an electric vehicle has attracted attention asone application destination of the wireless power supply system. Thepower receiver is mounted on the vehicle in this case. However, there isa limitation to improve driving accuracy (stop accuracy), and it isdifficult to park a vehicle in accurate alignment with a predeterminedposition for the purpose of charging. For this reason, there is apossibility of a positional relationship between the power-transmittingcoil and the power-receiving coil varying each time a vehicle is parked.When the relative positions of the power-transmitting coil and thepower-receiving coil deviate from a desired positional alignment, theefficiency of transmission may decrease due to a change in a couplingcoefficient between the coils.

In the related art, a technique for limiting a decrease in theefficiency of charging when a positional misalignment between coilsoccurs has been proposed (see, for example, Patent Document 1). A powersupply device (power transmitter) disclosed in Patent Document 1 changesthe frequency of AC power which is supplied from an inverter circuit(power source) to a power-transmitting coil, when the efficiency oftransmission decreases due to the occurrence of positional misalignment.The power supply device achieves an improvement in the efficiency ofcharging through this frequency change.

DOCUMENT OF RELATED ART Patent Document

[Patent Document 1] Japanese Unexamined Patent Application, FirstPublication No. 2012-130173

SUMMARY

As disclosed in Patent Document 1, impedance of the power-receiving sideseen from the inverter circuit is expressed by a function of thefrequency of electric power supplied to the power-transmitting coil andthe coupling coefficient between the power-transmitting coil and thepower-receiving coil. For this reason, by changing the frequency whenthe positional misalignment occurs and the coupling coefficient changes,a change in the coupling coefficient and the frequency incurs a changein impedance. The output AC voltage of the inverter circuit (orcorresponding input DC voltage of the inverter circuit) also changes inorder to supply desired electric power, due to such a change inimpedance.

When the output voltage of the inverter circuit becomes higher, it isnecessary to use an element having a high withstand voltage as, forexample, a circuit element of the power transmitter, and thus anincrease in the size of the element may be incurred. Note that thecircuit element of the power transmitter is, for example, a field effecttransistor (FET) as a switching element of the inverter circuit. Inaddition, when the output voltage of the inverter circuit becomes lower,an output current from the inverter circuit is required to be increasedin order to transmit desired electric power. In a case where the outputcurrent becomes larger, a Joule heat loss in an element or a wiringthrough which this current flows may increase, and the efficiency ofcharging may decrease.

In view of the above-described circumstances, an object of the presentdisclosure is to provide a wireless power supply system and a powerreceiver which are capable of suppressing a fluctuation in impedance ofa power-receiving side seen from a power source, when a couplingcoefficient changes.

A wireless power supply system according to one aspect of the presentdisclosure includes: a power transmitter; and a power receiver, thepower transmitter includes a power-transmitting coil to which AC powerof a frequency is input from a power source, the power receiverincludes: a power-receiving coil magnetically coupled to thepower-transmitting coil at a coupling coefficient; and a firstpower-receiving-side series element coupled in series to thepower-receiving coil and having imaginary impedance jZ_(S2i), and thefrequency, the coupling coefficient and the imaginary impedance aredetermined on the basis of satisfying the following formula,

$\begin{matrix}{{\frac{I_{2}}{I_{1}}} = {K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(1)}\end{matrix}$where L₁ is self-inductance of the power-transmitting coil, L₂ isself-inductance of the power-receiving coil, I₁ is a current flowingthrough the power-transmitting coil, I₂ is a current flowing through thepower-receiving coil, and K_(I) is a coefficient.

A power receiver according to another aspect of the present disclosurereceives electric power wirelessly from a power transmitter including apower-transmitting coil to which AC power of a frequency is input from apower source, and includes: a power-receiving coil magnetically coupledto the power-transmitting coil at a coupling coefficient; and a firstpower-receiving-side series element coupled in series to thepower-receiving coil and having imaginary impedance jZ_(S2i), and thefrequency, the coupling coefficient and the imaginary impedance aredetermined on the basis of satisfying the following formula,

$\begin{matrix}{{\frac{I_{2}}{I_{1}}} = {K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(9)}\end{matrix}$where L₁ is self-inductance of the power-transmitting coil, L₂ isself-inductance of the power-receiving coil, I₁ is a current flowingthrough the power-transmitting coil, I₂ is a current flowing through thepower-receiving coil, and K_(I) is a coefficient.

According to the present disclosure, it is possible to suppress afluctuation in impedance of a power-receiving side seen from a powersource, when a coupling coefficient changes.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a circuit diagram of a wireless power supply system accordingto a first embodiment of the present disclosure.

FIG. 2 is a diagram showing an installation example of apower-transmitting coil and a power-receiving coil of the wireless powersupply system according to the first embodiment of the presentdisclosure.

FIG. 3 is a functional block diagram of the wireless power supply systemaccording to the first embodiment of the present disclosure.

FIG. 4 is a circuit diagram of a wireless power supply system accordingto a second embodiment of the present disclosure.

FIG. 5 is a functional block diagram of the wireless power supply systemaccording to the second embodiment of the present disclosure.

FIG. 6 is a specific circuit diagram of the wireless power supply systemaccording to the second embodiment of the present disclosure.

FIG. 7 is a graph showing an example of a relationship between afrequency and a coupling coefficient according to the second embodimentof the present disclosure.

FIG. 8 is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the secondembodiment of the present disclosure.

FIG. 9A is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the secondembodiment of the present disclosure.

FIG. 9B is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the secondembodiment of the present disclosure.

FIG. 9C is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the secondembodiment of the present disclosure.

FIG. 9D is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the secondembodiment of the present disclosure.

FIG. 10 is a circuit diagram of a wireless power supply system accordingto a modification example of the present disclosure.

FIG. 11A is a graph showing an example of a relationship between afrequency and a coupling coefficient according to the modificationexample of the present disclosure.

FIG. 11B is a graph showing an example of a relationship between thefrequency and the coupling coefficient according to the modificationexample of the present disclosure.

FIG. 12 is an equivalent circuit of a power receiver according to themodification example of the present disclosure.

FIG. 13A is an example of a variable capacitor and a variable inductoraccording to the modification example of the present disclosure.

FIG. 13B is an example of a variable capacitor and a variable inductoraccording to the modification example of the present disclosure.

FIG. 13C is an example of a variable capacitor and a variable inductoraccording to the modification example of the present disclosure.

FIG. 13D is an example of a variable capacitor and a variable inductoraccording to the modification example of the present disclosure.

FIG. 14 is a circuit diagram of a wireless power supply system accordingto the modification example of the present disclosure.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present disclosure will be describedwith reference to the accompanying drawings.

First Embodiment

FIG. 1 is a circuit diagram of a wireless power supply system accordingto a first embodiment of the present disclosure. A wireless power supplysystem 100 includes a power transmitter 101 and a power receiver 103.The power transmitter 101 includes a power-transmitting coil 113described later, and the power receiver 103 include a power-receivingcoil 121 described later.

The power transmitter 101 transmits electric power to the power receiver103 wirelessly through magnetic coupling between the coils. A method oftransmitting electric power under magnetic coupling between coils is,for example, an electromagnetic induction method or a magnetic resonancemethod. Application examples of the wireless power supply system 100include, for example, charging systems or driving systems of movingobjects such as an electric vehicle (vehicle) or an underwater sailingbody, home electric appliances, or medical instruments. Thepower-transmitting coil 113 and the power-receiving coil 121 are, forexample, solenoid-type or circular-type coils. Meanwhile, thesolenoid-type is an aspect in which a conducting wire which forms a coilis helically wound in three-dimensional space. The circular-type coil isan aspect in which a conducting wire which forms a coil is spirallywound on a plane.

The power transmitter 101 includes the power-transmitting coil 113 towhich an AC power is input from a power source 111 that outputs AC powerof a frequency f, and an element (power-transmission-side serieselement) 115 having imaginary impedance. That is, the power-transmittingcoil 113 is configured to receive AC power of a frequency f from thepower source 111. The description of “AC power of a frequency f” meansthat a frequency of an AC voltage or an alternating current output fromthe power source 111 is f. The element 115 is coupled in series to thepower source 111 and the power-transmitting coil 113. Self-inductance ofthe power-transmitting coil 113 is denoted by L₁, and a current I₁(phasor current) flows through the power-transmitting coil 113.Meanwhile, the absolute value of a current displayed by phasor may be aneffective value, or may be a peak value.

The power source 111 is, for example, a power supply circuit such as aninverter circuit or an AC power source such as a commercially availablepower source, and outputs an AC voltage V_(S) (phasor voltage) of afrequency f (angular frequency ω).

AC power which is supplied power by the source 111 is received by thepower-transmitting coil 113 through the element 115. The invertercircuit can be realized by methods conventionally known such as ahalf-bridge method or a full-bridge method. Meanwhile, the absolutevalue of a voltage displayed by phasor may be an effective value, or maybe a peak value.

When the power source 111 is constituted by an inverter circuit, theinverter circuit includes a plurality of switching elements (such asfield effect transistors), and these elements are switched at aswitching frequency f, whereby AC power of the frequency f is outputfrom the power source 111. That is, a switching frequency is controlledin order to change the frequency of an inverter circuit output.

Meanwhile, in some configurations of inverter circuits, there may be acase where a frequency of an alternating current output from theinverter circuit does not coincide with a switching frequency. Inaddition, DC power is input to the inverter circuit, but this DC poweris, for example, power which is supplied from a DC power source or powerwhich is converted from AC power to DC power by a power conversioncircuit. The power conversion circuit includes, for example, arectifying function, and has a power factor correction (PFC) function ora voltage conversion function selectively. The voltage conversionfunction is realized by, for example, a non-insulation-type DC-DCconverter using a chopper circuit or an insulation-type DC-DC converterusing a transformer or the like.

The element 115 is constituted, for example, by a reactance element suchas an inductor (reactor, coil) or a capacitor, or a plurality ofelements of a combination of such reactance elements, and the imaginaryimpedance of the element 115 is denoted by jZ_(S1i) (j is an imaginaryunit and Z_(S1i) is an imaginary part). Hereinafter, the imaginary partis a real number. When the element 115 is constituted by a plurality ofelements, for example, it is possible to provide one element between oneterminal of the power source 111 and the coil 113 (in one coupling linebetween the power source 111 and the coil 113 of FIG. 1), and to provideone element between the other terminal of the power source 111 and thecoil 113 (in the other coupling line between the power source 111 andthe coil 113 of FIG. 1). In this case, the impedance of the element 115becomes equal to the synthetic impedance of these two elements. When theelement is a capacitor, the impedance of the element 115 is realized bya plurality of capacitors, and thus it is possible to reduce a voltagewhich is applied to each capacitor. Thus, it is possible to adopt acapacitor having a lower withstand voltage, and to reduce the size ofthe power transmitter 101.

The power receiver 103 includes the power-receiving coil 121 configuredto be magnetically coupled to the power-transmitting coil 113 at acoupling coefficient k, and an element (power-receiving-side serieselement) 123 having imaginary impedance. The element 123 is coupled inseries to the power-receiving coil 121. In addition, a load 125 havingreal impedance is coupled in series to the element 123. Self-inductanceof the power-receiving coil 121 is denoted by L₂, and a current I₂(phasor current) flows through the power-receiving coil 121.

There may by a case where a fluctuation range of the couplingcoefficient k due to the positional misalignment between thepower-transmitting coil 113 and the power-receiving coil 121 isdetermined in advance. For example, when the coupling coefficientbetween the power-transmitting coil 113 and the power-receiving coil 121becomes lower due to the positional misalignment, the power efficiencydecreases. For this reason, from the point of view of realizing desiredpower efficiency, a lower limit k_(min) of the coupling coefficient kwhich realizes the lowest allowable value of the power efficiency ispresent. An upper limit k_(max) of desired coupling coefficient k is amaximum value practicable for the wireless power supply system 100. Inaddition, when a range of the positional misalignment of the wirelesspower supply system 100 is determined in advance, the fluctuation rangeof the coupling coefficient k can be determined by obtaining thecoupling coefficient k of the wireless power supply system 100 withinthis range. Alternatively, the fluctuation range may be a use permissionrange within which the normal operation of the wireless power supplysystem 100 is guaranteed. This use permission range is described in, forexample, a specification sheet or a use manual.

The self-inductances of the power-transmitting coil 113 and thepower-receiving coil 121 may be changed according to the couplingcoefficient k. In this case, a changing range of the self-inductances ispresent according to change in the coupling coefficient within thefluctuation range. Accordingly, the self-inductances of thepower-transmitting coil 113 and the power-receiving coil 121 may be setto a value within the changing range. The self-inductances may be set tothe mean value of values within the changing range.

The element 123 is a component which is constituted by a reactanceelement such as an inductor (reactor, coil) or a capacitor, or aplurality of elements of a combination of such reactance elements. Theimaginary impedance of the element 123 is denoted by jZ_(S2i). The load125 is, for example, a power storage device (such as a lithium-ionsecondary battery, a nickel-hydrogen secondary battery, or ahigh-capacity electric double layer capacitor) that stores electricpower, or an electric device or an electronic device which is driven byelectric power. The real impedance of the load 125 is denoted by Z_(2r).Meanwhile, when the element 123 is constituted by a plurality ofelements, the synthetic impedance of these elements may be constitutedby imaginary impedance and real impedance. In this case, the imaginaryimpedance of the synthetic impedance is jZ_(S2i), and the synthesis ofthe real impedance of the synthetic impedance and the real impedance ofthe load 125 is Z_(2r).

In addition, when the power conversion circuit is coupled to thepower-receiving coil 121 in addition to a reactance element or asecondary battery, the real part of the synthetic impedance of thereactance element, the secondary battery, and the power conversioncircuit constitutes the real impedance Z_(2r) of the load 125, and theimaginary part constitutes the imaginary impedance Z_(S2i) of theelement 123. Meanwhile, the power conversion circuit can be constitutedby various circuits such as a rectifying circuit, or a combination ofthe rectifying circuit and a DC-DC converter.

The mutual inductance M between the power-transmitting coil 113 and thepower-receiving coil 121 satisfies the relational formula of M²=k²L₁L₂,and thus the circuit equation of FIG. 1 becomes Formula (10).

$\begin{matrix}{{\begin{bmatrix}{{j\;\omega\; L_{1}} + {jZ}_{S\; 1i}} & {j\;\omega\; k\sqrt{L_{1}L_{2}}} \\{j\;\omega\; k\sqrt{L_{1}L_{2}}} & {{j\;\omega\; L_{2}} + Z_{2r} + {jZ}_{S\; 2i}}\end{bmatrix}\begin{bmatrix}I_{1} \\I_{2}\end{bmatrix}} = \begin{bmatrix}V_{S} \\0\end{bmatrix}} & {{Formula}\mspace{14mu}(10)}\end{matrix}$

When a relational formula between currents I₁ and I₂ is determined fromFormula (10), Formula (11) is obtained.

$\begin{matrix}{\frac{I_{2}}{I_{1}} = {- \frac{j\;\omega\; k\sqrt{L_{1}L_{2}}}{Z_{2r} + {j\left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)}}}} & {{Formula}\mspace{14mu}(11)}\end{matrix}$

When Formula (12) is established, Formula (13) is established fromFormula (11) and Formula (12).

$\begin{matrix}{{\frac{I_{2}}{I_{1}}} = \sqrt{\frac{L_{1}}{L_{2}}}} & {{Formula}\mspace{14mu}(12)} \\{\frac{\omega^{2}k^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)^{2}} = 1} & {{Formula}\mspace{14mu}(13)}\end{matrix}$

Next, when impedance Z₁ (impedance which includes the power-transmittingcoil 113) of the power-receiving side seen from the power-transmittingcoil 113 is determined by Formula (10) and Formula (11), the impedanceZ₁ is represented by Formula (14). Meanwhile, V₁ in Formula (14)indicates a voltage which is applied to the power-transmitting coil. Inaddition, the description of “impedance of the power-receiving side seenfrom a component” means that, when the power-transmission side of thewireless power supply system is set to an upstream side, and thepower-receiving side of the wireless power supply system is a downstreamside, the impedance is “impedance on the downstream side from thiscomponent” (the same hereinafter).

                                 Formula  (14) $\begin{matrix}{Z_{1} = {\frac{V_{1}}{I_{1}} = {{j\;\omega\; L_{1}} + {j\;\omega\; k\sqrt{L_{1}L_{2}}\frac{I_{2}}{I_{1}}}}}} \\{= {{\frac{\omega^{2}k^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)^{2}}\frac{L_{1}}{L_{2}}Z_{2r}} -}} \\{j\frac{L_{1}}{L_{2}}\left( {{\frac{\omega^{2}k^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)^{2}}Z_{S\; 2i}} + {\left( {\frac{\omega^{2}k^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2\; i}} \right)^{2}} - 1} \right)\omega\; L_{2}}} \right)}\end{matrix}$

Each parameter (impedance of an element, frequency, and couplingcoefficient) of the wireless power supply system 100 is determined orcontrolled so that Formula (12) is established. In this case, Formula(13) is substituted into Formula (14), and thus Formula (14) becomesFormula (15).

$\begin{matrix}{Z_{1} = {\frac{L_{1}}{L_{2}}\left( {Z_{2r} - {jZ}_{S\; 2i}} \right)}} & {{Formula}\mspace{14mu}(15)}\end{matrix}$

Thus, impedance Z_(S) (impedance which does not include the power source111) of the power-receiving side seen from the power source 111 isrepresented by Formula (16).

$\begin{matrix}{Z_{S} = {\frac{L_{1}}{L_{2}}\left( {Z_{2r} + {j\left( {{\frac{L_{2}}{L_{1}}Z_{S\; 1i}} - Z_{S\; 2i}} \right)}} \right)}} & {{Formula}\mspace{14mu}(16)}\end{matrix}$

From Formula (16), the impedance Z_(S) of the power-receiving side seenfrom the power source 111 is represented by the real impedance Z_(2r) ofthe load 125 on the power-receiving side and the imaginary impedancesjZ_(S1i) and jZ_(S2i) of the elements 115 and 123, and does not containthe coupling coefficient k. Since the real impedance Z_(2r) and theimaginary impedances jZ_(S1i) and jZ_(S2i) are independent of thecoupling coefficient k, the impedance Z_(S) is also independent of thecoupling coefficient k. That is, when the frequency f is selected(determined) so that Formula (12) is established even when the couplingcoefficient changes, the impedance Z_(S) and the AC voltage V_(S)(=Z_(S)/I₁) does not fluctuate. The establishment of Formula (12) meansthat the combination of the frequency f, the coupling coefficient k, andthe imaginary impedance Z_(S2i) of the element 123 satisfies Formula(13). That is, whether Formula (12) is established has nothing to dowith the impedance of the element of the power transmitter 101. Inaddition, the real part of the impedance Z_(S) is represented only bythe impedance of the load 125 and the self-inductances of thepower-transmitting coil 113 and the power-receiving coil 121, and thusis not influenced by the impedances of the elements 115 and 123.

As a situation where the coupling coefficient k changes, for example,when a relative positional relationship between the power-transmittingcoil 113 and the power-receiving coil 121 (positional relationship in afront-and-rear direction which is the traveling direction of a vehicle Vand in a left-and-right direction which is the rotation direction(turning direction) of the vehicle V in FIG. 2) changes, the couplingcoefficient k changes. In addition, when a distance D between thepower-transmitting coil 113 and the power-receiving coil 121 (gapdistance in an up-and-down direction in FIG. 2) changes, the couplingcoefficient k changes. Further, when the direction or inclination of thepower-receiving coil 121 with respect to the power-transmitting coil 113changes, the coupling coefficient k changes. In these cases, a frequencyis selected so that Formula (13) is established at a couplingcoefficient after the change. Thereby, the impedance Z_(S) is notinfluenced by the coupling coefficient after the change, and thus it ispossible to suppress a fluctuation in the AC voltage V_(S). Hereinafter,positional misalignment is defined as follows: the power-transmittingcoil 113 or the power-receiving coil 121 deviates from a desiredposition; or the direction or inclination of the power-receiving coil121 with respect to the power-transmitting coil 113 deviates from adesired direction or inclination, in at least one direction of the threedirections (front-and-rear direction, left-and-right direction, andup-and-down direction).

The meaning that Formula (12) is established is not strictly limited tothe establishment of an equal sign relationship in Formula (12). Forexample, when an error range is determined in advance on the basis of ameasurement error, a control error, an allowable fluctuation range ofV_(S) specified in advance, or the like, and the difference between theratio of I₂ to I₁ and the square root of the ratio of L₁ to L₂ isincluded in the error range, Formula (12) can be regarded as beingestablished. Alternatively, when the difference is included in the errorrange, the impedance Z_(S) can be regarded as being independent of thecoupling coefficient k. In addition, the inductances L₁ and L₂ of thepower-transmitting coil 113 and the power-receiving coil 121 may changedepending on the relative positional relationship between thepower-transmitting coil and the power-receiving coil. For this reason, adeviation occurs between initial values L₁ and L₂ measured in advancebefore the supply of power and actual values L_(1r) and L_(2r) duringthe supply of power. For this reason, when a wireless power supplysystem is designed using the initial values L₁ and L₂ so that therelational formula of Formula (12) is satisfied, an error ε occurs as inFormula (17), in the relationship between the actual values L_(1r) andL_(2r) during the supply of power and coil currents. Meanwhile, a casewhere change in the inductances L₁ and L₂ of the power-transmitting coil113 and the power-receiving coil 121 has been taken up, but the currentI₁ and I₂ may change when the impedance jZ_(S2i) of the element 123changes, and thus Formula (17) is established.

$\begin{matrix}{{\frac{I_{2}}{I_{1}}} = {\sqrt{\frac{L_{1}}{L_{2}}} = {\left( {1 + ɛ} \right)\sqrt{\frac{L_{1r}}{L_{2r}}}}}} & {{Formula}\mspace{14mu}(17)}\end{matrix}$

In this case, the actual values during the supply of power, theimpedance Z₁ of the power-receiving side seen from thepower-transmitting coil 113 is represented by Formula (18), and theimpedance Z_(S) of the power-receiving side seen from the power source111 is represented by Formula (19). From Formula (19), even when theerror ε occurs, the impedance Z_(S) is independent of the couplingcoefficient k.

$\begin{matrix}{Z_{1} = {{\left( {1 + ɛ} \right)^{2}\frac{L_{1r}}{L_{2r}}Z_{2r}} - {j\frac{L_{1r}}{L_{2r}}\left( {{\left( {1 + ɛ} \right)^{2}Z_{S\; 2i}} + {\left( {\left( {1 + ɛ} \right)^{2} - 1} \right)\omega\; L_{2r}}} \right)}}} & {{Formula}\mspace{14mu}(18)} \\{Z_{S} = {{\left( {1 + ɛ} \right)^{2}\frac{L_{1r}}{L_{2r}}Z_{2r}} + {j\frac{L_{1r}}{L_{2r}}\left( {{\frac{L_{2r}}{L_{1r}}Z_{S\; 1i}} - {\left( {1 + ɛ} \right)^{2}Z_{S\; 2i}} - {\left( {\left( {1 + ɛ} \right)^{2} - 1} \right)\omega\; L_{2r}}} \right)}}} & {{Formula}\mspace{14mu}(19)}\end{matrix}$

The fact that the impedance Z_(S) is independent of the couplingcoefficient k and that the AC voltage V_(S) from the power source 111 isnot likely to fluctuate means that the voltage on the power-transmissionside (for example, voltage V₁ between both ends of thepower-transmitting coil 113) having a correlation with the AC voltageV_(S) is not like to fluctuate likewise. In addition, when the powersource 111 is constituted by an inverter circuit, the input DC voltageand the output AC voltage of the inverter circuit operate in conjunctionwith each other. Therefore, the fact that the output AC voltage V_(S) isnot likely to fluctuate means that the input DC voltage is not likely tofluctuate likewise. When the power conversion circuit that outputs thisDC voltage includes a chopper circuit, the output terminal of the powerconversion circuit includes a capacitor, but a fluctuation in the DCvoltage from the power conversion circuit is suppressed, therebyallowing the withstand voltage of this capacitor to be reduced.Therefore, it is possible to reduce the size of the capacitor, and toreduce the size of the power transmitter 101.

Further in Formula (16), when the imaginary impedance Z_(S1i) satisfiesFormula (20), the imaginary part of Formula (16) is canceled, and theimpedance Z_(S) has only a real part as in Formula (21). In this case,the power factor of the power source 111 is 100%. On the other hand, thevalue of the imaginary impedance Z_(S1i) is shifted from the value ofFormula (20), and thus the power factor can be set to a desired valuewithout the impedance Z_(S) depending on the coupling coefficient k.

$\begin{matrix}{Z_{S\; 1i} = {\frac{L_{1}}{L_{2}}Z_{S\; 2i}}} & {{Formula}\mspace{14mu}(20)} \\{Z_{S} = {\frac{L_{1}}{L_{2}}Z_{2r}}} & {{Formula}\mspace{14mu}(21)}\end{matrix}$

Subsequently, reference will be made to FIG. 3 to describe a specificcontrol method of how to change a frequency when the couplingcoefficient between the coils changes. FIG. 3 is a functional blockdiagram of the wireless power supply system according to the firstembodiment of the present disclosure.

First, the functional blocks of the power transmitter 101 will bedescribed. The power transmitter 101 includes an AC power output portion141, a power transmission portion 143, a power-transmission-sidedetector 145, a power-transmission-side communication portion 147, astorage portion 148, and a power-transmission-side controller 149. TheAC power output portion 141 is coupled to the power transmission portion143, the power transmission portion 143 is coupled to thepower-transmission-side detector 145, and the power-transmission-sidecontroller 149 is coupled to the AC power output portion 141, thepower-transmission-side detector 145, the power-transmission-sidecommunication portion 147 and the storage portion 148. Meanwhile, the ACpower output portion 141 can also be provided outside of the powertransmitter 101. In addition, the function of each functional block isrealized by hardware. Specifically, the function of the powertransmission portion 143 can be realized by a power-transmission device,the function of the power-transmission-side detector 145 can be realizedby a power-transmission-side detection device, the function of thepower-transmission-side communication portion 147 can be realized by apower-transmission-side communication device, the function of thestorage portion 148 can be realized by a memory, and the function of thepower-transmission-side controller 149 can be realized by apower-transmission-side control device.

The AC power output portion 141 is equivalent to the power source 111 ofFIG. 1, and outputs AC power. In addition, the power transmissionportion 143 is equivalent to the power-transmitting coil 113 and theelement 115 of FIG. 1, and sends electric power to a power receivingportion 151 of the power receiver 103 described later.

The power-transmission-side detector 145 is a current sensor thatdetects the current I₁ flowing through the power-transmitting coil 113,as a value indicating the power-transmission situation of the powertransmission portion 143, and sends data of the detected current to thepower-transmission-side controller 149. An example of the current sensorcapable of being used includes a sensor that measures a magnetic field,generated in the vicinity of a power cable through which a currentpasses, on the basis of a Hall effect, or a sensor that has a resistorinserted into a power cable through which a current passes and measuresa potential drop occurring in this resistor.

The power-transmission-side communication portion 147 performs radiocommunication with a power-receiving-side communication portion 155described later. A system of communication between thepower-transmission-side communication portion 147 and thepower-receiving-side communication portion 155 is, for example, radiocommunication using radio waves of ZigBee (Registered Trademark),Bluetooth (Registered Trademark) or the like, or optical communicationusing an optical signal. In a case of the communication system usingradio waves, the power-transmission-side communication portion 147includes an antenna. In a case of the communication system using anoptical signal, the power-transmission-side communication portion 147includes a light emitting element or a light receiving element forcommunication.

The storage portion 148 stores various information such as informationrelating to the coupling coefficient or the impedance (value such as L₁or L₂) of the element, a program which describes each function of thepower-transmission-side controller 149 described later, and the like,and is constituted by a volatile recording medium such as a randomaccess memory (RAM) or a non-volatile recording medium such as a readonly memory (ROM). The information relating to the coupling coefficientrefers to, for example, information required for specifying the couplingcoefficient between the power-transmitting coil 113 and thepower-receiving coil 121, or information of a combination of thefrequency f with the coupling coefficient k when Formula (12) issatisfied.

The power-transmission-side controller 149 controls and manages eachfunctional block of the power transmitter 101, and the entirety of thepower transmitter 101. The power-transmission-side controller 149 isconstituted by, for example, any suitable processor such as a centralprocessing portion (CPU), or a dedicated processor (for example, digitalsignal processor (DSP)) specialized for each process. Specific processeswhich are performed by the power-transmission-side controller 149 willbe described later.

Next, the functional blocks of the power receiver 103 will be described.The power receiver 103 includes a power receiving portion 151, apower-receiving-side detector 153, a power-receiving-side communicationportion 155, and a power-receiving-side controller 157. The powerreceiving portion 151 is coupled to the power-receiving-side detector153, and the power-receiving-side detector 153 and thepower-receiving-side communication portion 155 are coupled to thepower-receiving-side controller 157. In addition, the function of eachfunctional block is realized by hardware. Specifically, the function ofthe power receiving portion 151 can be realized by a power receivingdevice, the function of the power-receiving-side detector 153 can berealized by a power-receiving side detection device, the function of thepower-receiving-side communication portion 155 can be realized by apower-receiving-side communication device, and the function of thepower-receiving-side controller 157 can be realized by apower-receiving-side control device. As is the case with the powertransmitter 101, the power receiver 103 also includes a storage portionthat stores a program which describes each function of thepower-receiving-side controller 157, and the like, but the storageportion is not shown in the drawing.

The power receiving portion 151 is equivalent to the power-receivingcoil 121 and the element 123 of FIG. 1, receives electric powertransmitted from the power transmission portion 143, and supplies theelectric power to the load 125.

The power-receiving-side detector 153 is a current sensor that detectsthe current I₂ flowing through the power-receiving coil 121, as a valueindicating the power-receiving situation of the power receiving portion151, and sends data of the detected current to the power-receiving-sidecontroller 157. An example of the current sensor capable of being usedincludes a sensor that measures a magnetic field, generated in thevicinity of a power cable through which a current passes, on the basisof a Hall effect, or a sensor that has a resistor inserted into a powercable through which a current passes and measures a potential dropoccurring in this resistor.

The power-receiving-side communication portion 155 performs radiocommunication with the power-transmission-side communication portion147. In a case of the communication system using radio waves, thepower-receiving-side communication portion 155 includes an antenna. In acase where the communication system using an optical signal, thepower-receiving-side communication portion 155 includes a light emittingelement or a light receiving element for communication.

The power-receiving-side controller 157 controls and manages eachfunctional block of the power receiver 103, and the entirety of thepower receiver 103. The power-receiving-side controller 157 isconstituted by, for example, any processor such as a CPU or a DSP.Specific processes which are performed by the power-receiving-sidecontroller 157 will be described later.

Subsequently, a description will be given of specific control contentsof the power-transmission-side controller 149 and thepower-receiving-side controller 157 when a coupling coefficient changesdue to positional misalignment. Hereinafter, a coupling coefficient whenthere is no positional misalignment is denoted by k₁, and a frequencysatisfying Formula (12) in that case is denoted by f₁. The storageportion 148 stores these values in association with each other.

On the assumption that the positional misalignment does not occur, thepower-transmission-side controller 149 controls the AC power outputportion 141 so as to output AC power of the frequency f₁ equivalent tothe absence of the positional misalignment. The power transmissionportion 143 sends this AC power to the power receiving portion 151. Inaddition, the power-transmission-side detector 145 detects the currentI₁ flowing through the power-transmitting coil 113, and sends its datato the power-transmission-side controller 149. On the other hand, thepower-receiving-side detector 153 detects the current I₂ flowing throughthe power-receiving coil 121, and sends its data to thepower-receiving-side controller 157. The power-receiving-side controller157 controls the power-receiving-side communication portion 155 so as totransmit the received current data to the power transmitter 101.

Then, the power-transmission-side communication portion 147 receivescurrent data from the power-receiving-side communication portion 155,and sends the current data to the power-transmission-side controller149. The power-transmission-side controller 149 reads out the values ofL₁ and L₂ stored in the storage portion 148, and determines whetherFormula (12) is established, from the read-out values of L₁ and L₂ andthe received data of I₁ and I₂.

When Formula (12) is established, the power-transmission-side controller149 determines that the power-transmitting coil 113 and thepower-receiving coil 121 have a desired positional relationship, andthat there is no positional misalignment therebetween. Thepower-transmission-side controller 149 controls the AC power outputportion 141 so as to continue to output the AC power of the frequency f₁without changing a frequency.

When Formula (12) is not established, the power-transmission-sidecontroller 149 determines that the relative positional relationshipbetween the power-transmitting coil 113 and the power-receiving coil 121deviates from a desired position. Since the currents flowing through thecoils 113 and 121 change due to the positional misalignment, thepower-transmission-side controller 149 calculates the amount of change a(a is a value larger or smaller than 1) in the currents from I₁ and I₂which are detection values and L₁ and L₂ which are storage values (seeFormula (22)).

$\begin{matrix}{\alpha = {{\frac{I_{2}}{I_{1}}} \div \sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(22)}\end{matrix}$

When the impedances of the element and the load are constant in theright side of Formula (11), a parameter which changes due to thepositional misalignment is only the coupling coefficient. That is, sincethe amount of change a corresponds to the amount of change in thecoupling coefficient, a coupling coefficient k₂ after the positionalmisalignment is determined to a value represented by Formula (23).k ₂ =αk ₁  Formula (23)

Thus, the power-transmission-side controller 149 reads out the value ofthe coupling coefficient k₁ which is stored in the storage portion 148,determines a coupling coefficient k₂ after the positional misalignmentby Formula (23), and calculates a frequency f₂ satisfying Formula (12)at the coupling coefficient k₂, from Formula (13). Thepower-transmission-side controller 149 controls the AC power outputportion 141 so as to output the AC power of this frequency f₂.

As shown above, an example of the specific control method of thefrequency change has been described. Hereinafter, as a modificationexample, a method of changing a frequency without using thepower-transmission-side detector 145 will be described. Functional blockdiagrams in this case are the same as those in FIG. 3, except for thepower-transmission-side detector 145 being omitted. Hereinafter, adescription will be given with a focus on that different from the above.The functions of the functional blocks 141, 143, 147, 151, and 155 arethe same as those described above, and thus the description will not berepeated.

The storage portion 148 stores a relationship between the couplingcoefficient and power reception in the power receiver 103, asinformation relating to the coupling coefficient. This relationship is,for example, a relationship between the coupling coefficient and power(supplied power) supplied to the load 125 when the AC power outputportion 141 outputs constant electric power at a predetermined frequency(since a frequency is fixed when the coupling coefficient isdetermined). Hereinafter, information relating to the couplingcoefficient stored in the storage portion 148 is a relationship betweenthe power reception and the coupling coefficient, but there is nolimitation to such an aspect. As the information relating to thecoupling coefficient, a parameter having a correlation with the couplingcoefficient can be arbitrarily used. The parameter having a correlationwith the coupling coefficient is, for example, the current I₂ of thepower-receiving coil 121.

The power-receiving-side detector 153 is a voltage sensor and a currentsensor that detect a voltage which is applied to the load 125 and acurrent which is input to the load 125, as a power-receiving situation.Meanwhile, a detection location is not limited load 125, and thepower-receiving-side detector 153 may measure a voltage and a currentrelating to the element 123. In addition, a detection target is notlimited to the voltage and the current, and the detection target may bea power. In this case, the power-receiving-side detector 153 is a powersensor. An example of the voltage sensor includes a sensor that dividesa voltage using a resistor and converts the voltage into a digital valueusing an AD converter. In addition, an example of the power sensorincludes a sensor that measures a voltage and a current using thevoltage sensor and the current sensor, and temporally averages a valueobtained by multiplying the voltage and the current together todetermine electric power.

When the power transmitter 101 outputs the AC power of the frequency f₁,the power receiving portion 151 receives this electric power, and thepower-receiving-side detector 153 detects a voltage and a currentrelating to the load 125 and sends its data to the power-receiving-sidecontroller 157. The power-receiving-side controller 157 calculates apower value which is charged (consumed) in the load 125 from thereceived data. The power-receiving-side controller 157 controls thepower-receiving-side communication portion 155 so as to transmit thispower value data to the power transmitter 101.

The power-transmission-side communication portion 147 receives the powervalue data from the power-receiving-side communication portion 155. Thepower-transmission-side controller 149 reads out the relationshipbetween the power reception and the coupling coefficient which arestored in the storage portion 148, and determines whether the read-outpower value corresponding to the coupling coefficient k₁ and thereceived power value data are coincident with each other. Meanwhile, thewording “coincident with each other” is not limited strictly to theestablishment of the equality, and the power-transmission-sidecontroller 149 can also regard the read-out power value and the receivedpower value as being coincident with each other insofar as thedifference therebetween is in an error range which is determined inadvance.

When these power values are coincident with each other, thepower-transmission-side controller 149 determines that thepower-transmitting coil 113 and the power-receiving coil 121 have adesired positional relationship, and that there is no positionalmisalignment therebetween. The power-transmission-side controller 149controls the AC power output portion 141 so as to continue to output theAC power of the frequency f₁ without changing the frequency.

When these power values are not coincident with each other, thepower-transmission-side controller 149 determines that the relativepositional relationship between the power-transmitting coil 113 and thepower-receiving coil 121 deviates from a desired position, and specifiesthe coupling coefficient k₂ corresponding to the received power valuedata from the relationship (for example, relationship between the powerreception and the coupling coefficient) stored in the storage portion148. The power-transmission-side controller 149 calculates a frequencyf₂ satisfying Formula (12) at the coupling coefficient k₂, and controlsthe AC power output portion 141 so as to output the AC power of thisfrequency f₂.

As described above, in the wireless power supply system 100 of thepresent embodiment, when the coupling coefficient k changes, thefrequency f and the imaginary impedance jZ_(S2i) of the element 123 aredetermined so that the impedance Z_(S) of the power-receiving side seenfrom the power source 111 is independent of the coupling coefficient k,on the basis of satisfying the Formula (12). That is, in the presentembodiment, the wireless power supply system 100 satisfies Formula (12),thereby the impedance Z_(S) is represented by the real impedance Z_(2r)and the imaginary impedances jZ_(S1i) and jZ_(S2i) of the load 125, andis independent of the coupling coefficient k. For this reason, when thecoupling coefficient k changes due to a positional misalignment betweenthe power-transmitting coil 113 and the power-receiving coil 121 or achange in the distance between the coils, the power-transmission-sidecontroller 149 selects the frequency f so that Formula (12) isestablished. That is, the power-transmission-side controller 149 isconfigured to perform the following. When the coupling coefficient kchanges, the power-transmission-side controller 149 regulates thefrequency f so that the impedance Z_(S) of the power-receiving side seenfrom the power source 111 is independent of the coupling coefficient k.By changing the frequency f in this manner, a case does not occur inwhich the impedance Z_(S) changes due to a change in the couplingcoefficient k, and thus it is possible to suppress a fluctuation in theimpedance Z_(S). It is possible to suppress a fluctuation in the ACvoltage V_(S) to such an extent that the impedance Z_(S) is not likelyto fluctuate.

In the present embodiment, the element 115 of the power transmitter 101and the element 123 of the power receiver 103 can be set so as tosatisfying Formula (20). In this case, the impedance Z_(S) does not havean imaginary part, and not only the impedance Z_(S) of thepower-receiving side seen from the power source 111 is independent ofthe coupling coefficient, but also the power factor of the power source111 is 100%. Thus, it is possible to maximize a power-transmissionefficiency in the power source 111. In this case, since the impedance ofthe power-transmission side seen from the power-receiving side is alsodetermined to pure resistance (resistance having none of inductance andcapacitance), electric power can be transmitted from the load 125 to thepower source 111 with the same efficiency as the efficiency of powertransmission from the power source 111 to the load 125. That is, it ispossible to perform bidirectional power transmission.

As in the present embodiment, designing the wireless power supply system100 so that Formula (12) is established has an advantage when mutualcompatibility between a plurality of power receivers or between aplurality of power transmitters is secured. For example, a descriptionwill be given of a case where the power transmitter 101 and the powerreceiver 103 where Formula (12) is established are designed, and a powerreceiver (second power receiver) for supplying electric power to a load(second load) of impedance Z_(2ra) different from the load 125 isrequired to be designed (the circuit configuration of the second powerreceiver is the same as that of the power receiver 103, and only theelement impedance of the second power receiver is different from that ofthe power receiver 103). In this case, β=Z_(2ra)/Z_(2r) is determined,and self-inductance L_(2a) of a power-receiving coil (a secondpower-receiving coil corresponding to the power-receiving coil 121) ofthe second power receiver and imaginary impedance jZ_(S2ia) of anelement (second element corresponding to the element 123) are determinedso as to satisfy Formula (24) and Formula (25).L _(2a) =βL ₂  Formula (24)Z _(S2ia) =βZ _(S2i)  Formula (25)

In this case, when the power transmitter 101 and the second powerreceiver are combined, the impedance Z_(S) of the power-receiving sideseen from the power source 111 is determined to a value represented byFormula (16). That is, the second power receiver is realized so thatFormula (24) and Formula (25) are established, and thus the impedance ofthe power-receiving side seen from the power source 111 can be keptconstant without changing the power transmitter 101. Thereby, even whenthe impedance of the load changes, a wireless power supply system inwhich a voltage on the power-transmission side is likely to fluctuatecan be constructed through a simple design change.

Similarly, even when the same electric power as that in a case of thepower source 111 is required to be supplied to the load 125 from a powersource (second power source) that outputs a voltage V_(Sa) which isdifferent from the power source 111, a power transmitter (hereinafter,second power transmitter) to which the voltage V_(Sa) is supplied can beconfigured through a simple design change (the circuit configuration ofthe second power transmitter is the same as that of the powertransmitter 101, and only the element impedance of the second powertransmitter is different from that of the power transmitter 101).Specifically, in order for the second power source to output the samepower P as that of the power source 111, the impedance Z_(Sa) of thepower-receiving side seen from the second power source is required tosatisfy Formula (26).

$\begin{matrix}{Z_{Sa} = {\frac{V_{Sa}^{2}}{P} = {\frac{V_{Sa}^{2}}{V_{S}^{2}}Z_{S}}}} & {{Formula}\mspace{14mu}(26)}\end{matrix}$

When the relation of γ=(V_(Sa)/V_(S))² is established, self-inductanceL_(1a) of a power-transmitting coil (second power-transmitting coilcorresponding to the power-transmitting coil 113) of the second powertransmitter and imaginary impedance jZ_(S1ia) of an element (thirdelement corresponding to the element 115) satisfy Formula (27) andFormula (28), and thus Formula (26) is satisfied.L _(1a) =γL ₁  Formula (27)Z _(S1ia) +γZ _(S1i)  Formula (28)

That is, the second power transmitter is realized so that Formula (27)and Formula (28) are established, and thus a constant voltage can besupplied to the load 125 without changing the power receiver 103.Thereby, even when the voltage of the power source changes, a wirelesspower supply system in which a voltage on the power-transmission side islikely to fluctuate can be constructed through a simple design change.

Second Embodiment

In the first embodiment, a description has been given of a case wherethe element 115 having imaginary impedance is coupled in series to thepower-transmitting coil 113, and the element 123 having imaginaryimpedance is coupled in series to the power-receiving coil 121. In asecond embodiment, a description will be given of a case where elementshaving imaginary impedance are coupled in parallel to apower-transmitting coil and a power-receiving coil.

A wireless power supply system 200 according to the second embodimentincludes a power transmitter 201 and a power receiver 203. The powertransmitter 201 includes a power-transmitting coil 213 to which AC poweris input from a power source 211, an element (power-transmission-sideseries element) 215, and an element (power-transmission-side parallelelement) 217. The power receiver 203 includes a power-receiving coil221, an element (power-receiving-side series element) 223, and anelement (power-receiving-side parallel element) 227. A load 225 iscoupled in series to the element 223. These components 211, 213, 215,221, 223, and 225 are the same as the components 111, 113, 115, 121,123, and 125, respectively, of the power transmitter 101 and the powerreceiver 103 according to the first embodiment, and thus the descriptionwill not be repeated. The following description shows that the impedanceZ_(S) (impedance which does not include the power source 211) of thepower-receiving side seen from the power source 211 is independent ofthe coupling coefficient in the circuit of FIG. 4. Meanwhile, as shownin FIG. 5, the wireless power supply system 200 includes an AC poweroutput portion 241, a power transmission portion 243, apower-transmission-side detector 245, a power-transmission-sidecommunication portion 247, a storage portion 248, apower-transmission-side controller 249, a power receiving portion 251, apower-receiving-side detector 253, a power-receiving-side communicationportion 255 and a power-receiving-side controller 257. The functions ofthe respective function portions are the same as the functions of thefunction portions according to the first embodiment which correspondthereto, and thus the description will not be repeated. In addition, ina change control method of a frequency, the same method as that in thefirst embodiment can also be used.

The element 217 is coupled in parallel to the power-transmitting coil213 and coupled to the power-transmitting coil side rather than theelement 215, and has imaginary impedance jZ_(P1i). That is, the element217 is coupled in parallel to the power-transmitting coil 213 at aposition closer to the power-transmitting coil 213 than the element 215,and has imaginary impedance jZ_(P1i). To express such a couplingrelationship in other words, the element 215 is coupled in series to thepower-transmitting coil 213 at a position closer to the power source 211than the element 217. In addition, the element 227 is coupled inparallel to the power-receiving coil 221 and coupled to thepower-receiving coil side rather than the element 223, and has imaginaryimpedance jZ_(P2i). That is, the element 227 is coupled in parallel tothe power-receiving coil 221 at a position closer to the power-receivingcoil 221 than the element 223, and has imaginary impedance jZ_(P2i). Theelements 217 and 227 are constituted, for example, by a reactanceelement such as an inductor (reactor, coil) or a capacitor, or aplurality of elements of a combination of such elements.

When the circuit equation of FIG. 4 is set up, Formula (29) isestablished.

$\mspace{650mu}{{{Formula}\mspace{14mu}{{(29)\begin{bmatrix}{{j\;\omega\; L_{1}} + {j\frac{Z_{S\; 1i}Z_{P\; 1i}}{Z_{S\; 1i} + Z_{P\; 1i}}}} & {j\;\omega\; k\sqrt{L_{1}L_{2}}} \\{j\;\omega\; k\sqrt{L_{1}L_{2}}} & {{j\;\omega\; L_{2}} + \frac{{jZ}_{P\; 2i}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)}{Z_{2r} + {jZ}_{S\; 2i} + {jZ}_{P\; 2i}}}\end{bmatrix}}\begin{bmatrix}I_{1} \\I_{2}\end{bmatrix}}} = {\quad\begin{bmatrix}{\frac{Z_{p\; 1i}}{Z_{S\; 1i} + Z_{p\; 1i}}V_{S}} \\0\end{bmatrix}}}$

As in the first embodiment, each parameter of the wireless power supplysystem 200 is determined or controlled so that Formula (12) isestablished. In this case, the result of determining the impedance Z₁(impedance which includes the element 217) of the power-receiving sideseen from the element 217 is determined to a value represented byFormula (30), and this formula does not contain the coupling coefficientk.

$\begin{matrix}{Z_{1} = {\frac{L_{1}}{L_{2}}\frac{Z_{P\; 1i}{Z_{P\; 2i}\left( {Z_{2r} - {jZ}_{S\; 2i}} \right)}}{{Z_{P\; 1i}Z_{P\; 2i}} + {\left( {Z_{P\; 1i} - {\frac{L_{1}}{L_{2}}Z_{P\; 2i}}} \right)\left( {Z_{S\; 2i} + {jZ}_{2r}} \right)}}}} & {{Formula}\mspace{14mu}(30)}\end{matrix}$

When the impedance values of the power-transmission-side parallelelement 217 and the power-receiving-side parallel element 227 aredetermined so that Formula (31) is established, Formula (32) isestablished from Formula (30) and Formula (31).

$\begin{matrix}{Z_{P\; 1i} = {\frac{L_{1}}{L_{2}}Z_{P\; 2i}}} & {{Formula}\mspace{14mu}(31)} \\{Z_{1} = {\frac{L_{1}}{L_{2}}\left( {Z_{2r} - {jZ}_{S\; 2i}} \right)}} & {{Formula}\mspace{14mu}(32)}\end{matrix}$

Thus, the impedance Z_(S) of the power-receiving side seen from thepower source 211 is determined to a value represented by Formula (33).

$\begin{matrix}{Z_{S} = {\frac{L_{1}}{L_{2}}\left( {Z_{2r} + {j\left( {{\frac{L_{2}}{L_{1}}Z_{S\; 1i}} - Z_{S\; 2i}} \right)}} \right)}} & {{Formula}\mspace{14mu}(33)}\end{matrix}$

According to Formula (33), when Formula (12) and Formula (31) areestablished, the impedance Z_(S) of the power-receiving side seen fromthe power source 211 is represented by the real impedance Z_(2r) of theload 225 on the power-receiving side and the imaginary impedancesjZ_(S1i) and jZ_(S2i) of the elements 215 and 223. Since the realimpedance Z_(2r) of the load 225 and the imaginary impedances jZ_(S1i)and jZ_(S2i) are independent of the coupling coefficient k, theimpedance Z_(S) is also independent of the coupling coefficient k. Inaddition, a real part of the impedance Z_(S) is represented only by theimpedance of the load 225 and self-inductances of the power-transmittingcoil 213 and the power-receiving coil 221, and is not influenced byimpedances of the elements 215, 217, 223 and 227.

Further, when the imaginary impedance Z_(S1i) satisfies Formula (34),the imaginary part of Formula (33) is canceled, and the impedance Z_(S)has only a real part as in Formula (35). In this case, the power factorof the power source 211 is 100%. On the other hand, the value of theimaginary impedance Z_(S1i) is shifted from the value of Formula (34),and thus the power factor can be determined to a desired value withoutthe impedance Z_(S) depending on the coupling coefficient k.

$\begin{matrix}{Z_{S\; 1i} = {\frac{L_{1}}{L_{2}}Z_{S\; 2i}}} & {{Formula}\mspace{14mu}(34)} \\{Z_{S} = {\frac{L_{1}}{L_{2}}Z_{2r}}} & {{Formula}\mspace{14mu}(35)}\end{matrix}$

A description will be given of a case where the circuit of FIG. 4 isconstituted by more specific circuit elements. Specifically, as shown inFIG. 6, the elements 215 and 223 are constituted by inductors (havingself-inductances of L_(S1) and L_(S2)), and the elements 217 and 227 areconstituted by capacitors (having capacitances of C_(P1) and C_(P2)).

In this case, a relationship between the capacitances of the elements217 and 227 is represented by Formula (36) from Formula (31). WhenFormula (12) and Formula (36) are established, the real part of theimpedance Z_(S) of the power-receiving side seen from the power source211 is independent of the coupling coefficient k.

$\begin{matrix}{C_{P\; 1} = {\frac{L_{2}}{L_{1}}C_{P\; 2}}} & {{Formula}\mspace{14mu}(36)}\end{matrix}$

In addition, a relationship between the self-inductances of the elements215 and 223 is represented by Formula (37) from Formula (34). WhenFormula (12), Formula (36) and Formula (37) are established, the powerfactor of the power source 211 is 100%.

$\begin{matrix}{L_{S\; 1} = {\frac{L_{1}}{L_{2}}L_{S\; 2}}} & {{Formula}\mspace{14mu}(37)}\end{matrix}$

A description will be given of a relationship between the couplingcoefficient k and the frequency f satisfying Formula (12) in the circuitconfiguration of FIG. 6. When the ratio of a current I₂ to a current I₁is determined from the circuit equation of FIG. 6, the ratio isdetermined to a value represented by Formula (38).

$\begin{matrix}{\frac{I_{2}}{I_{1}} = \frac{{- j}\;\omega\; k\sqrt{L_{1}L_{2}}}{{j\;\omega\; L_{2}} + \frac{\frac{1}{j\;\omega\; C_{P\; 2}}\left( {Z_{2r} + {j\;\omega\; L_{S\; 2}}} \right)}{Z_{2r} + {j\;\omega\; L_{S\; 2}} + \frac{1}{j\;\omega\; C_{P\; 2}}}}} & {{Formula}\mspace{14mu}(38)}\end{matrix}$

When Formula (38) satisfies Formula (12), Formula (39) is established.Meanwhile, the asterisk “*” in Formula (39) indicates a complexconjugate.

$\begin{matrix}{k^{2} = \frac{\begin{matrix}\left( {{j\;\omega\; L_{2}} + \frac{\frac{1}{j\;\omega\; C_{P\; 2}}\left( {Z_{2r} + {j\;\omega\; L_{S\; 2}}} \right)}{Z_{2r} + {j\;\omega\; L_{S\; 2}} + \frac{1}{j\;\omega\; C_{P\; 2}}}} \right) \\\left( {{j\;\omega\; L_{2}} + \frac{\frac{1}{j\;\omega\; C_{P\; 2}}\left( {Z_{2r} + {j\;\omega\; L_{S\; 2}}} \right)}{Z_{2r} + {j\;\omega\; L_{S\; 2}} + \frac{1}{j\;\omega\; C_{P\; 2}}}} \right)^{*}\end{matrix}}{\omega^{2}L_{2}^{2}}} & {{Formula}\mspace{14mu}(39)}\end{matrix}$

When the impedances of the elements and the load are fixed, the couplingcoefficient k is a function of an angular frequency ω (that is,frequency f), and this function is represented by a solid-line graph G1of FIG. 7. Meanwhile, a broken-line graph G2 of FIG. 7 which is acomparison target indicates a result in a case the element 223 of thepower receiver 203 is constituted by only the capacitor rather than theinductor. The element 223 being constituted by the inductor rather thanthe element 223 being constituted by only the capacitor obtains a resultof the magnitude of the inclination of the graph becoming larger, thatis, the change range of the coupling coefficient k satisfying Formula(12) becomes larger by changing the frequency f.

A description will be given of a case where, for example, as therestriction of the power source 211 or the entire wireless power supplysystem 200, the variable range (f_(min)(lower limit)≤f≤f_(max)(upperlimit)) of the frequency f is determined, and this variable range isdetermined as in FIG. 7 with respect to the graphs G1 and G2. Thevariable range is determined by, for example, the upper and lower limitsof the frequency range of power capable of being output by the powersource 211. When the coupling coefficient becomes a value denoted by k₃of FIG. 7 due to the positional misalignment between thepower-transmitting coil and the power-receiving coil, or the like, afrequency f₃₋₁ satisfying Formula (12) is included within the variablerange in the graph G1. On the other hand, in the graph G2, a frequencyf₃₋₂ satisfying Formula (12) lies outside of the variable range. Thatis, when the power-receiving-side series element 223 of the powerreceiver 203 is constituted by the inductor, a frequency satisfyingFormula (12) is more likely to be present within the variable range thanwhen the element is constituted by the capacitor even when the couplingcoefficient changes greatly. Thereby, it is possible to change afrequency while suppressing fluctuation in an AC voltage from the powersource 211, in response to a change in the coupling coefficient in awider range.

When at least one of the self-inductance L_(S2) of the element 223(inductor) and the capacitance C_(P2) of the element 227 (capacitor) canbe set to any given value, the shape of the graph G1 changes with achange in a setting value. For example, when the value of theself-inductance L_(S2) is selected so that the coupling coefficientmonotonically decreases or monotonically increases in the variablerange, the change range of the coupling coefficient k becomes largerthan when the minimum value of the coupling coefficient is located inthe variable range. Particularly, when a relationship between thecoupling coefficient k and the frequency f satisfying Formula (12) isasymmetric centering on the minimum value of the coupling coefficient(asymmetric with respect to a line parallel to the axis (vertical axis)of the coupling coefficient of FIG. 8 through this minimum value) asshown in FIG. 8, it is preferable that the variable range of thefrequency f is located in a region (in FIG. 8, a monotonicallydecreasing region, or the left side of the minimum value) having alarger absolute value of an inclination.

When the fluctuation range of the coupling coefficient is present, theimpedances of the element 223 and element 227 are determined so that thecoupling coefficient is determined to the upper limit k_(max) or thelower limit k_(min) of the fluctuation range when the frequency is theupper limit f_(max) or the lower limit f_(min) of the variable range, asshown in FIGS. 9A through 9D.

That is, in the wireless power supply system 200 of the presentembodiment, the imaginary impedances of the element 223 and element 227are determined so as to satisfy Formula (12) when the frequency is theupper limit f_(max) or the lower limit f_(min) of the variable range,and the coupling coefficient is the upper limit k_(max) or the lowerlimit k_(min) of the fluctuation range. In Formula (12), as theself-inductances of the power-transmitting coil 213 and thepower-receiving coil 221, any of values in the changing range of theself-inductance which depends on change in the coupling coefficient kwithin the fluctuation range is used. By making such a determination, itis possible to increase the possibility of the frequency f satisfyingFormula (12) being present when the coupling coefficient changes.Meanwhile, FIG. 9A shows a case where the coupling coefficient isdetermined to the lower limit k_(min) of the fluctuation range when thefrequency is the upper limit f_(max) of the variable range. FIG. 9Bshows a case where the coupling coefficient is determined to the lowerlimit k_(min) of the fluctuation range when the frequency is the lowerlimit f_(min) of the variable range.

FIG. 9C shows a case where the coupling coefficient is determined to theupper limit k_(max) of the fluctuation range when the frequency is thelower limit f_(min) of the variable range. FIG. 9D shows a case wherethe coupling coefficient is determined to the upper limit k_(max) of thefluctuation range when the frequency is the upper limit f_(max) of thevariable range.

Further, when a relationship between the frequency f and the couplingcoefficient k satisfying Formula (12) is determined to a relationshiprepresented by a graph monotonically increasing or monotonicallydecreasing (for example, graph of FIG. 8 monotonically decreasing) inthe variable range of the frequency f, a change control method of afrequency can be performed more easily than the method described in thefirst embodiment. The method in the first embodiment is a method ofdetermining the coupling coefficient k₂ after a change from Formula(23), and calculating the frequency f₂ satisfying Formula (12) fromFormula (13). On the other hand, hereinafter, a description will begiven of a method of determining the frequency f₂ without using Formula(13). Specifically, Formula (12) is established at the time of theestablishment of α=1 from Formula (20), and thus thepower-transmission-side controller 249 performs feedback control so thata is 1. For example, the power-transmission-side controller 249determines a on the basis of the values of currents I₁ and I₂ detectedby the power-transmission-side detector 245 and the power-receiving-sidedetector 253, and performs PID control on a difference between α and 1.Since the polynomial of Formula (13) is not required to be solved, it ispossible to limit the computational load of the power-transmission-sidecontroller 249.

As described above, in the present embodiment, the frequency f, thecoupling coefficient k, and the imaginary impedance of thepower-receiving-side series element 223 satisfy Formula (12), and thusthe impedance Z_(S) of the power-receiving side seen from the powersource 211 is independent of the coupling coefficient k. In addition,the power-transmission-side parallel element 217 and thepower-receiving-side parallel element 227 satisfy Formula (31), and thusthe impedance Z_(S) is represented by the same formula as that in thefirst embodiment and is not influenced by the impedance values of theelements 217 and 227. When the coupling coefficient k changes due to thepositional misalignment between the power-transmitting coil 213 and thepower-receiving coil 221 or a change in a distance between the coils,the frequency f can be selected so that Formula (12) is established.That is, the power-transmission-side controller 249 is configured toregulate the frequency f so that the impedance Z_(S) of thepower-receiving side seen from the power source 211 is independent ofthe coupling coefficient k, when the coupling coefficient k changes.Thereby, by changing the frequency f, a case does not occur in which theimpedance Z_(S) changes due to a change in the coupling coefficient k,and thus it is possible to suppress fluctuation in the impedance Z_(S).Thus, it is possible to suppress fluctuation in the AC voltage V_(S) tosuch an extent that the impedance Z_(S) is not likely to fluctuate.

In the present embodiment, the power-receiving-side series element 223can be constituted by the inductor.

When the power receiver 203 includes a power conversion circuit undersuch a configuration, the power-receiving-side series element 223 playsa role in a harmonic reduction filter, and thus the waveform of analternating current which is supplied to the load 225 can be broughtclose to an ideal sine wave.

In the present embodiment, the power-receiving-side series element 223can be constituted by the inductor, and the power-receiving-sideparallel element 227 can be constituted by the capacitor. Thereby, themagnitude of the inclination of the graph indicating a relationshipbetween the frequency f and the coupling coefficient k satisfyingFormula (12) can be made larger than when both the power-receiving-sideseries element 223 and the power-receiving-side parallel element 227 areconstituted by the capacitors. Thus, it is possible to correspond to awider fluctuation range of the coupling coefficient k in a finitevariable range of the frequency f.

Although the present disclosure has been described on the basis of thedrawings or embodiments, those skilled in the art can perform additions,omissions, substitutions, and other modifications of configurationswithin the claims of the present application, that is, without departingfrom the spirit of the present disclosure. The present disclosure is notto be considered as limited by the foregoing description and is onlylimited by the scope of the appended claims.

In the embodiments of the present disclosure, the element configurations(FIGS. 1 and 4) of two aspects have been described, but the presentdisclosure is not limited to these aspects. For example, as shown inFIG. 10, a power transmitter may include an element 319 which is coupledin series to a power-transmitting coil 313 and coupled to thepower-transmitting coil side rather than a power-transmission-sideparallel element 317, and a power receiver may include an element 329which is coupled in series to a power-receiving coil 321 and coupled tothe power-receiving coil side rather than a power-receiving-sideparallel element 327. That is, the element 319 is coupled in series tothe power-transmitting coil 313 at a position closer to thepower-transmitting coil 313 than the power-transmission-side parallelelement 317. The element 329 is coupled in series to the power-receivingcoil 321 at a position closer to the power-receiving coil 321 than thepower-receiving-side parallel element 327. The elements 319 and 329include imaginary impedances jZ_(S1i-2) and jZ_(S2i-2), respectively. Asin the first and second embodiments, when a circuit equation is solved,and Formula (12), Formula (31) and Formula (40) are established, Formula(33) is established. Thereby, the impedance Z_(S) is configured so asnot to be influenced by the coupling coefficient k (so as to beindependent). In the example of the circuit configuration as shown inFIG. 10, each of the elements 315 and 323 is an inductor, and each ofthe elements 317, 319, 327, and 329 is a capacitor. In a furthermodification example, a further element (not shown) may be coupled inparallel or series to the power-transmitting coil 313 between thepower-transmission-side series element 315 and the power-transmittingcoil 313, and a further element (not shown) may be coupled in parallelor series to the power-receiving coil 321 between thepower-receiving-side series element 323 and the power-receiving coil321. Even in this case, the impedance Z_(S) can be made independent ofthe coupling coefficient k. Specifically, the element configurations ofthe power transmitter 301 and the power receiver 303 may be set to besymmetric with respect to each other on the basis of thepower-transmitting coil 313 and the power-receiving coil 321(line-symmetric with respect to a straight line which is located in themiddle of the power-transmitting coil 313 and the power-receiving coil321 of FIG. 10 and is orthogonal to the power-transmission direction ofboth the coils), and the impedance of the element on thepower-transmission side may be (L₁/L₂) times the impedance of thesymmetric element on the power-receiving side (see Formula (40)).

$\begin{matrix}{Z_{{S\; 1i} - 2} = {\frac{L_{1}}{L_{2}}Z_{{S\; 2i} - 2}}} & {{Formula}\mspace{14mu}(40)}\end{matrix}$

In the description of the aforementioned embodiment of the presentdisclosure, a fluctuation in the impedance Z_(2r) of the load is notconsidered. However, for example, when the load is constituted by abattery, the impedance Z_(2r) of the load (battery) fluctuates dependingon the state of charge (SOC) of the battery. In this case, the real partof the impedance Z_(S) of the power-receiving side seen from the powersource represented by Formula (16) or Formula (33) changes according toa fluctuation in the impedance Z_(2r) of the load. However, even in sucha configuration, the impedance Z_(S) being independent of the couplingcoefficient is the same as that in the aforementioned embodiments.

Further, since the impedance Z_(2r) is contained in the relationalformula between the coupling coefficient k and the frequency f shown inFormula (39), a fluctuation in the impedance Z_(2r) of the load givesrise to a change in the shape of the graph shown in FIG. 7 or 8.However, a combination (hereinafter, referred to as a singular solution)of the coupling coefficient k and the frequency f satisfying Formula(12) is present irrespective of the impedance Z_(2r). Hereinafter, thesingular solution in the circuit configuration of FIG. 4 will bedescribed. For convenience of description, each of the elements 215,217, 223, and 227 of the circuit configuration shown in FIG. 4 is acapacitor, and the capacitances of the elements 215, 217, 223, and 227are denoted by C_(S1), C_(P1), C_(S2), and C_(P2), respectively.Meanwhile, some of these elements may be constituted by inductors. Inaddition, the presence of the singular solution is not limited to thecircuit configuration of FIG. 4, and a singular solution can bedetermined likewise in the circuit configuration of FIG. 10.

When the relational formula of the currents I₁ and I₂ is determined fromFormula (29), and Formula (12) is established, Formula (41) isestablished. Meanwhile, the relations of Z_(S1i)=−1/(ωC_(S1)),Z_(P1i)=−1/(ωC_(P1)), Z_(S2i)=−1/(ωC_(S2)), and Z_(P2i)=−1/(ωC_(P2)) areestablished.

$\begin{matrix}{{\frac{\omega^{2}{L_{2}^{2}\left( {{\omega^{4}C_{S\; 2}^{2}C_{P\; 2}^{2}Z_{2r}^{2}} + {\omega^{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}^{2}} \right)}}{\left( {\left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}}} \right)^{2} + {\omega^{2} C_{S\; 2}^{2}{Z_{2r}^{2}\left( {1 - {\omega^{2}L_{2}C_{P\; 2}}} \right)}^{2}}} \right)}k^{2}} = 1} & {{Formula}\mspace{14mu}(41)}\end{matrix}$

When Formula (41) is rearranged, Formula (42) is obtained.(1−ω² L ₂(C _(S2) +C _(P2)))²−ω⁴ L ₂ ²(C _(S2) +C _(P2))² k ²+(ω² C_(S2) ²(1−ω² L ₂ C _(P2))²−ω⁶ L ₂ ² C _(S2) ² C _(P2) ² k ²)Z _(2r)²=0   Formula (42)

When Formula (43) is established, Formula (42) is establishedirrespective of the value of Z_(2r).(1−ω² L ₂(C _(S2) +C _(P2)))²−ω⁴ L ₂ ²(C _(S2) +C _(P2))² k ²=0ω² C _(S2) ²(1−ω² L ₂ C _(P2))²−ω⁶ L ₂ ² C _(S2) ² C _(P2) ² k ²=0  Formula (43)

When Formula (43) is solved, a positive solution and a negative solutionare obtained as the solutions of the capacitances C_(S2) and C_(P2), butthe actual capacitances C_(S2) and C_(P2) have positive values, and thusthe positive solution is adopted. Meanwhile, the negative solution meansthat the element 223 is an inductor rather than a capacitor.

When the inductance of the power-receiving coil 121 is known, apredetermined frequency and a predetermined coupling coefficient aresubstituted into Formula (43), to thereby obtain the impedance of theelement in which the predetermined frequency and the predeterminedcoupling coefficient are the singular solution. For example, the valueof the predetermined frequency substituted into Formula (43) isdetermined to the upper limit f_(max) or the lower limit f_(min) of thevariable range, and the value of the predetermined coupling coefficientis determined to the lower limit k_(min) of the fluctuation range. Inthis manner, the singular solution can be arranged at the boundary ofthe variable range.

Subsequently, reference will be made to FIGS. 11A and 11B to describe achange in the shape of a graph of the coupling coefficient k and thefrequency f when the impedance Z_(2r) of the load 225 fluctuates. First,as shown in FIG. 11A, a description will be given of a case where asingular solution S1 is within the variable range of the frequency f(except the boundary), and is within the fluctuation range of thecoupling coefficient k (except the boundary). When the impedance Z_(2r)of the load 225 increases, the graph of the coupling coefficient k andthe frequency f changes from a graph G3 to a graph G4. Meanwhile, adescription will be given of a case where, when f_(max) is determined asthe initial value of the frequency, the coupling coefficient is denotedby k₅ (>k_(min)). In this case, in the graph G3, the frequency f₅satisfying Formula (12) is found by reducing the frequency. On the otherhand, in the graph G4, it is necessary to increase the frequency, butthe frequency is not able to be determined to be higher than f_(max) andthus it is not possible to select a frequency satisfying Formula (12).For this reason, when the coupling coefficient satisfying Formula (12)is k₆ at f_(max) in the graph G4, it is not possible to select afrequency satisfying Formula (12) at the coupling coefficient k(k_(min)≤k<k₆). When the actual coupling coefficient k (k_(min)≤k<k₆) issmaller than the coupling coefficient k₆ satisfying Formula (12) at thefrequency f_(max), the impedance Z_(S) of the power-receiving side seenfrom the power source 111 is determined to a capacitive load. When thepower source 111 is constituted by an inverter circuit, it is notpossible to realize soft switching.

As shown in FIG. 11B, a description will be given of a case where asingular solution S2 is the upper limit f_(max) of the variable range ofthe frequency f, and is the lower limit k_(min) of the fluctuation rangeof the coupling coefficient k. When the impedance Z_(2r) of the load 225increases, the graph of the coupling coefficient k and the frequency fchanges from the graph G3 to a graph G5. In this case, when thefrequency is f_(max), and the coupling coefficient is k₅, a frequencyf₅₋₁ satisfying Formula (12) is found by reducing the frequency in thegraph G3. In addition, in the graph G5, a frequency f₅₋₂ satisfyingFormula (12) is also found by reducing the frequency. Unlike FIG. 11A,it is possible to select a frequency satisfying Formula (12) even whenthe coupling coefficient k is within of a range of k_(min)≤k<k₆.Therefore, it is possible to increase the range of the couplingcoefficient satisfying Formula (12) in the variable range of thefrequency f. In addition, since the actual coupling coefficient k isdetermined to be equal to or larger than the coupling coefficientk_(min) satisfying Formula (12) at the frequency f_(max), the impedanceZ_(S) of the power-receiving side seen from the power source 111 isdetermined to an inductive load. When the power source 111 isconstituted by an inverter circuit, it is possible to realize softswitching. Further, even when the graph changes due to a fluctuation inthe impedance Z_(2r), it is possible to select a frequency satisfyingFormula (12) through the same control of a decrease in frequency.

In the aforementioned embodiment of the present disclosure, thepower-transmission efficiency of the power source of the powertransmitter has been described, but it is also necessary to increaseefficiency inside the power receiver in order to improve the powerefficiency of the entire wireless power supply system. Hereinafter, animprovement in efficiency inside the power receiver will be examinedwith reference to FIG. 4. For convenience of description, each of theelements 223 and 227 of the circuit configuration shown in FIG. 4 is acapacitor, and the capacitances of the elements 223 and 227 are denotedby C_(S2) and C_(P2), respectively.

An electromotive force V_(m) is induced to the power-receiving coil 221by magnetic coupling to the power-transmitting coil 213, and the powerreceiver 203 is represented by an equivalent circuit as shown in FIG.12. The electromotive force V_(m) is represented by Formula (44).V _(m) =jωk√{square root over (L ₁ L ₂)}I ₁  Formula (44)

In addition, the circuit equation of FIG. 12 is represented by Formula(45).

$\begin{matrix}{{j\;\omega\; k\sqrt{L_{1}L_{2}}I_{1}} + {\quad{{\left( {{j\;\omega\; L_{2}} + \frac{{\omega^{2}C_{S\; 2}^{2}Z_{2r}^{2}} - {j\;{\omega\left( {\left( {C_{S\; 2} + C_{P\; 2}} \right) + {\omega^{2}C_{S\; 2}^{2}C_{P\; 2}Z_{2r}^{2}}} \right)}}}{{\omega^{4}C_{P\; 2}^{2}C_{S\; 2}^{2}Z_{2r}^{2}} + {\omega^{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}^{2}}} \right)I_{2}} = 0}}} & {{Formula}\mspace{14mu}(45)}\end{matrix}$

When Formula (44) is substituted into Formula (45) and a current I₂ issolved, Formula (46) is derived.

$\begin{matrix}{I_{2} = {{- \frac{\begin{pmatrix}{{\omega^{2}C_{S\; 2}^{2}Z_{2r}} +} \\\begin{matrix}{j\;{\omega\left( {{\omega^{2}C_{S\; 2}^{2}C_{P\; 2}{Z_{2r}^{2}\left( {1 - {\omega^{2}L_{2}C_{P\; 2}}} \right)}} +} \right.}} \\\left. {\left( {C_{S\; 2} + C_{P\; 2}} \right)\left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}}} \right)} \right)\end{matrix}\end{pmatrix}}{\begin{matrix}{\left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}}} \right)^{2} +} \\{\omega^{2}C_{S\; 2}^{2}{Z_{2r}^{2}\left( {1 - {\omega^{2}L_{2}C_{P\; 2}}} \right)}^{2}}\end{matrix}}}V_{m}}} & {{Formula}\mspace{14mu}(46)}\end{matrix}$

In order to increase the efficiency inside the power receiver, a phasedifference between the electromotive force induced to thepower-receiving coil 221 and the current I₂ of the power-receiving coil221 may be brought close to 0°. Thus, when the phase difference is 0°,and the imaginary part of Formula (46) is not present, the efficiencyinside the power receiver becomes largest. This is equivalent to a casewhere Formula (47) is established. In this case, when desired electricpower is supplied to the load 225, reactive power inside the powerreceiver is not present. Therefore, it is possible to reduce the currentof the power-receiving coil, and to limit the generation of heat in anelement or a wiring.ω² C _(S2) ² C _(P2) Z _(2r) ²(1−ω² L ₂ C _(P2))+(C _(S2) +C _(P2))(1−ω²L _(2r)(C _(S2) +C _(P2)))=0   Formula (47)

A conditional formula for increasing the efficiency inside the powerreceiver is derived in the circuit configuration of FIG. 10 in a similarmanner without being derived with the limitation of the circuitconfiguration of FIG. 4.

In the circuit configuration of FIG. 4, when the impedance of thepower-receiving coil 221 is determined in advance, and any given valueis selected with each of the frequency f (angular frequency ω), thecoupling coefficient k and the impedance Z_(2r) of the load, variablesare two impedances of the elements 223 and 227. Therefore, when twoconditional formulas of Formula (41) which is an establishment conditionof Formula (12) and Formula (47) which is a maximum efficiency conditionare given, each of the impedances of the element 223 and 227 isdetermined to a specific value. That is, considering the establishmentcondition of Formula (12) and the maximum efficiency condition, adesired frequency f and a desired coupling coefficient k do not satisfyFormula (43). In addition, when the singular solution is determined to adesired value, each of the impedances of the elements 223 and 227 isdetermined to a specific value in Formula (43), and thus the maximumefficiency condition is not satisfied simultaneously.

On the other hand, in the circuit configuration of FIG. 10, the element329 is provided in addition to the elements 323 and 327, and thus thenumber of variables is three. For convenience of description, each ofthe elements 323, 327, and 329 of the circuit configuration of FIG. 10is a capacitor, and the capacitances of the elements 323, 327, and 329are denoted by C_(S2), C_(P2), and C_(Sf2), respectively. When Formula(12) is established, Formula (48) is established similarly to Formula(41), and Formula (49) to which a singular solution is given is obtainedfrom Formula (48). In addition, similarly to a case of the circuitconfiguration of FIG. 4, Formula (50) is obtained as the maximumefficiency condition.

$\begin{matrix}{\mspace{79mu}{{\frac{\omega^{2}{L_{2}^{2}\left( {{\omega^{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}^{2} + {\omega^{4}C_{P\; 2}^{2}C_{S\; 2}^{2}Z_{2r}^{2}}} \right)}}{\begin{matrix}{{\omega^{2}C_{S\; 2}^{2}{Z_{2r}^{2}\left( {1 - {\omega^{2}L_{2}C_{P\; 2}} + \frac{C_{P\; 2}}{C_{{Sf}\; 2}}} \right)}^{2}} +} \\\left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}} + \frac{\left( {C_{S\; 2} + C_{P\; 2}} \right)}{C_{{Sf}\; 2}}} \right)^{2}\end{matrix}}k^{2}} = 1}} & {{Formula}\mspace{14mu}(48)} \\{{{\omega^{4}L_{2}^{2}{k^{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}^{2}} - \left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}} + \frac{\left( {C_{S\; 2} + C_{P\; 2}} \right)}{C_{{Sf}\; 2}}} \right)^{2}} = 0} & {{Formula}\mspace{14mu}(49)} \\{\mspace{79mu}{{{\left( {1 - {\omega^{2}L_{2}C_{P\; 2}} + \frac{C_{P\; 2}}{C_{{Sf}\; 2}}} \right)^{2} - {\omega^{4}L_{2}^{2}k^{2}C_{P\; 2}^{2}}} = 0}{{{\left( {C_{S\; 2} + C_{P\; 2}} \right)\left( {1 - {\omega^{2}{L_{2}\left( {C_{S\; 2} + C_{P\; 2}} \right)}} + \frac{\left( {C_{S\; 2} + C_{P\; 2}} \right)}{C_{{Sf}\; 2}}} \right)} + {\left( {1 - {\omega^{2}C_{P\; 2}L_{2}} + \frac{C_{P\; 2}}{C_{{Sf}\; 2}}} \right)\omega^{2}C_{S\; 2}^{2}C_{P\; 2}Z_{2r}^{2}}} = 0}}} & {{Formula}\mspace{14mu}(50)}\end{matrix}$

Since variables are three impedances of the elements 323, 327, and 329,and conditional formulas are total three of two formulas in Formula (49)and one formula in Formula (50), each of the impedances of the elements323, 327, and 329 satisfying the maximum efficiency condition isdetermined to a specific value while the singular solution is determinedto a desired value. In addition, even when there is a separate conditionother than the maximum efficiency condition for setting anycharacteristics, by combining this separate condition and Formula (49),and the impedance of an element satisfying the separate condition isdetermined while the singular solution is determined to a desired value.For example, when the impedance of the element 329 is determined to be acertain value, each of the impedances of the elements 323 and 327satisfying Formula (49) is determined to a specific value. Therefore,when it is difficult to define a desired condition as a formula, it ispossible to confirm whether the desired condition is satisfied in a casewhere the impedance of the element 329 is a certain value. When thedesired condition is not satisfied, it is possible to adjust theimpedance of the element 329 so that the desired condition is satisfiedby changing the impedance of the element 329.

In the description of the aforementioned embodiment of the presentdisclosure, it has been assumed that the impedance of the element isfixed and does not change, but the present disclosure is not limited tosuch an aspect. For example, the element of the power receiver may beconstituted by a variable element (variable inductor or variablecapacitor). In this case, the impedance of the power-receiving side seenfrom the power source can made to be independent of the couplingcoefficient by changing the impedance (imaginary impedance) of theelement of the power receiver rather than the frequency f, or bychanging the impedance (imaginary impedance) of the element of the powerreceiver as well as the frequency f when the coupling coefficient kchanges. Meanwhile, the control of change in the imaginary impedance ofthe element may be performed by the aforementionedpower-transmission-side controller. In this case, thepower-transmission-side controller is configured to perform thefollowing. Specifically, when the coupling coefficient k changes, thepower-transmission-side controller can specify the value of theimaginary impedance of the element so that the impedance of thepower-receiving side seen from the power source is independent of thecoupling coefficient k. The power-transmission-side controller caninstruct the power-receiving-side controller to set the imaginaryimpedance of the element to this value through the communicationportion.

In the description of the aforementioned embodiment or modificationexample of the present disclosure, the frequency or the imaginaryimpedance of the element is controlled and changed by thetransmission-side controller. However, the aforementionedpower-receiving-side controller may be configured to control and changethe frequency or the imaginary impedance of the element.

In this case, the power-receiving-side controller may acquireinformation required to the control from the transmission-sidecontroller through the aforementioned communication portion. That is,when the coupling coefficient k changes, the power-receiving-sidecontroller can specify the value of the frequency of AC power which isoutput by the power source so that the impedance of the power-receivingside seen from the power source is independent of the couplingcoefficient k. The power-receiving-side controller can instruct thepower-transmission-side controller to set the frequency of the AC powerwhich is output by the power source to this value. In addition, when thecoupling coefficient k changes, the power-receiving-side controller mayregulate the imaginary impedance of the element of the power receiver sothat the impedance of the power-receiving side seen from the powersource is independent of the coupling coefficient k.

Further, the wireless power supply system of the present disclosure maybe configured such that operational effects of the embodiment or themodification example are obtained. Therefore, when the couplingcoefficient k changes, the wireless power supply system of the presentdisclosure may be configured to regulate at least one of the frequencyof the AC power which is output by the power source and the imaginaryimpedance of the element so that the impedance of the power-receivingside seen from the power source is independent of the couplingcoefficient k.

As shown in FIGS. 13A through 13D, an example of a variable capacitor ora variable inductor is a circuit in which a plurality of capacitors 431a through 431 d or inductors 433 a through 433 d having differentimpedances are coupled to each other through switching elements SW1 toSW6. By power-receiving-side controller switching the switching elementsSW1 through SW6, it is possible to switch elements which are used amongthe capacitors 431 a through 431 d and the inductors 433 a through 433d, and to change the values of the capacitance and inductance of thecircuit. The value of the capacitance or inductance of the circuitchanges, and thus a relationship between the frequency f and thecoupling coefficient k satisfying Formula (12) changes. Therefore, bychanging the value of the capacitance or inductance of the circuit, itis possible to increase the range of the coupling coefficient ksatisfying Formula (12) in the variable range of the frequency f. Inaddition, the variable capacitor or the variable inductor may includenot only a circuit in which the value of capacitance or inductancechanges selectively and discontinuously as shown in FIGS. 13A through13D, but also a circuit in which the above value changes continuously asin a variable transformer, a trimmer capacitor or the like.

In the description of the embodiment of the present disclosure, it isassumed that the voltage or the current in the wireless power supplysystem is a sine wave. However, when the voltage or the current is not asine wave and contains a plurality of frequency components, the presentdisclosure can be applied to a fundamental wave component.

When resistive components are present in the power-transmitting coil,the power-receiving coil and each element, the resistive components aredisregarded to consider the power-transmitting coil, the power-receivingcoil and each element as ideal inductance (coil) or capacitance, andthus the present disclosure can be used. Further, even when theresistive components and reactance components are present in wiringswithin the wireless power supply system, these resistive components andreactance components are disregarded, and thus the present disclosurecan be used.

In the description of the embodiment of the present disclosure,application examples of the wireless power supply system includecharging systems or driving systems of moving objects, home electricappliances or medical instruments, but the present disclosure is notlimited to such an aspect. The present disclosure can be applied to, forexample, various circuit devices which use the principle ofelectromagnetic induction of coils. Specifically, the wireless powersupply system of the present disclosure can be incorporated into aninsulation-type DC-DC converter.

In the description of the embodiment of the present disclosure, when acoupling coefficient changes, each parameter (the impedance of anelement and the frequency) of the wireless power supply system isdetermined so that Formula (12) is established, but the presentdisclosure is not limited to such an aspect. Specifically, when thecoupling coefficient changes, each parameter (the impedance of anelement and the frequency) of the wireless power supply system may bedetermined so that Formula (51) is established.

$\begin{matrix}{{\frac{I_{2}}{I_{1}}} = {K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(51)}\end{matrix}$

First, a description will be provided with reference to the circuitconfiguration of FIG. 1. When Formula (51) is established, Formula (52)is established from Formula (11) and Formula (51). Meanwhile, K_(I) is acoefficient (constant) which is determined in advance.

$\begin{matrix}{\frac{\omega^{2}k^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)^{2}} = K_{I}^{2}} & {{Formula}\mspace{14mu}(52)}\end{matrix}$

Each parameter (the impedance of the element, the frequency, and thecoupling coefficient) of the wireless power supply system 100 isdetermined or controlled so that Formula (51) is established. In thiscase, Formula (52) is substituted into Formula (14), and thus Formula(14) becomes Formula (53).

$\begin{matrix}{Z_{1} = {\frac{L_{1}}{L_{2}}\left( {{K_{I}^{2}Z_{2r}} - {j\left( {{K_{I}^{2}Z_{S\; 2i}} + {\left( {K_{I}^{2} - 1} \right)\omega\; L_{2}}} \right)}} \right)}} & {{Formula}\mspace{14mu}(53)}\end{matrix}$

Thus, the impedance Z_(S) of the power-receiving side seen from thepower source 111 is represented by Formula (54).

$\begin{matrix}{Z_{S} = {\frac{L_{1}}{L_{2}}\left( {{K_{I}^{2}Z_{2r}} + {j\left( {{\frac{L_{2}}{L_{1}}Z_{S\; 1i}} - \left( {{K_{I}^{2}Z_{S\; 2i}} + {\left( {K_{I}^{2} - 1} \right)\omega\; L_{2}}} \right)} \right)}} \right)}} & {{Formula}\mspace{14mu}(54)}\end{matrix}$

From Formula (54), the impedance Z_(S) of the power-receiving side seenfrom the power source 111 does not contain the coupling coefficient k.Therefore, the impedance Z_(S) is independent of the couplingcoefficient k. That is, even when the coupling coefficient changes, thefrequency f is selected (determined) so that Formula (51) isestablished, and thus the impedance Z_(S) is independent of the couplingcoefficient k. That is, since the coefficient K_(I) is constant and doesnot change, the right side of Formula (51) is a constant value.Therefore, the frequency f and the imaginary impedance Z_(S2i) aredetermined so that the ratio of I₂ to I₁ keeps constant even when thecoupling coefficient changes. As a result, the impedance Z_(S) and theAC voltage V_(S) (=Z_(S)/I₁) are not likely to fluctuate. Meanwhile,similar to other embodiments, when the element 123 of the power receiver103 is a variable element, the impedance Z_(S2i) of the element 123rather than the frequency f may be changed so that Formula (51) isestablished. That is, when the frequency f, the imaginary impedanceZ_(S2i) and the coupling coefficient k are values which satisfy Formula(51), the impedance Z_(S) is independent of the coupling coefficient k.

Further, in Formula (54), when the imaginary impedance Z_(S1i) satisfiesFormula (55), the imaginary part of Formula (54) is canceled, and theimpedance Z_(S) has only a real part as in Formula (56). In this case,the power factor of the power source 111 is 100%. On the other hand, thevalue of the imaginary impedance Z_(S1i) is shifted from the value ofFormula (55), and thus the power factor can be determined to a desiredvalue without the impedance Z_(S) depending on the coupling coefficientk.

$\begin{matrix}{Z_{S\; 1i} = {\frac{L_{1}}{L_{2}}\left( {{K_{I}^{2}Z_{S\; 2i}} + {\left( {K_{I}^{2} - 1} \right)\omega\; L_{2}}} \right)}} & {{Formula}\mspace{14mu}(55)} \\{Z_{S} = {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{2r}}} & {{Formula}\mspace{14mu}(56)}\end{matrix}$

Meanwhile, when the frequency f is shifted from the value whichsatisfies Formula (51), Formula (57) is established. ε is an error.

$\begin{matrix}{{\frac{I_{2}}{I_{1\;}}} = {\left( {1 + ɛ} \right)K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(57)}\end{matrix}$

In this case, the impedance Z₁ of the power-receiving side seen from thepower-transmitting coil 113 is represented by Formula (58), and theimpedance Z_(S) of the power-receiving side seen from the power source111 is represented by Formula (59).

From Formula (59), even when the error ε occurs, the impedance Z_(S) isindependent of the coupling coefficient k.

$\begin{matrix}{Z_{1} = {{{K_{I}^{2}\left( {1 + ɛ} \right)}^{2}\frac{L_{1}}{L_{2\;}}Z_{2r}} - {{{jK}_{I}^{2}\left( {1 + ɛ} \right)}^{2}\frac{L_{1}}{L_{2\;}}Z_{S\; 2i}} - {j\;\frac{L_{1}}{L_{2\;}}\left( {{K_{I}^{2}\left( {1 + ɛ} \right)}^{2} - 1} \right)\omega\; L_{2}}}} & {{Formula}\mspace{14mu}(58)} \\{Z_{S} = {{{K_{I}^{2}\left( {1 + ɛ} \right)}^{2}\frac{L_{1}}{L_{2\;}}Z_{2r}} - {{{jK}_{I}^{2}\left( {1 + ɛ} \right)}^{2}\frac{L_{1}}{L_{2\;}}Z_{S\; 2i}} - {j\;\frac{L_{1}}{L_{2\;}}\left( {{K_{I}^{2}\left( {1 + ɛ} \right)}^{2} - 1} \right)\omega\; L_{2}} + j}} & {{Formula}\mspace{14mu}(59)}\end{matrix}$

When the imaginary impedance Z_(S1i) satisfies Formula (55), Formula(59) becomes Formula (60). When Formula (60) is compared with Formula(56), shifting of the frequency f from a value which satisfies Formula(51) means that it is possible to control the real part of the impedanceZ_(S) and the power factor. In addition, by selecting the frequency f sothat Formula (57) is satisfied, constant electric power can be suppliedto the load 125 even when the parameters (for example, the inductancesL₁ and L₂) fluctuate or the load 125 fluctuates.

$\begin{matrix}{Z_{S} = {{{K_{I}^{2}\left( {1 + ɛ} \right)}^{2}\frac{L_{1}}{L_{2\;}}Z_{2r}} + {{jK}_{I}^{2}\frac{L_{1}}{L_{2\;}}\left( {1 - \left( {1 + ɛ} \right)^{2}} \right)\left( {Z_{S\; 2i} - {\omega\; L_{2}}} \right)}}} & {{Formula}\mspace{14mu}(60)}\end{matrix}$

Subsequently, a description will be provided with reference to thecircuit configuration of FIG. 14. The circuit configuration of FIG. 14is a circuit configuration obtained by adding an element 519 to thecircuit configuration of FIG. 4. That is, components 511, 513, 515 and517 of a power transmitter 501 and components 521, 523 and 527 of apower receiver 503 of FIG. 14 are the same as the components 211, 213,215 and 217 of the power transmitter 201 and the components 221, 223 and227 of the power receiver 203 of FIG. 4, respectively. Further, a load525 coupled to the power receiver 503 is the same as the load 225coupled to the power receiver 203.

The description of these components is the same as the description ofFIG. 4, and thus the description of these components will not berepeated.

The element 519 is coupled in series to the power-transmitting coil 513and coupled to the power-transmitting coil side rather than the element517, and has imaginary impedance jZ_(S1i-2). That is, the element 519 iscoupled in series to the power-transmitting coil 513 at a positioncloser to the power-transmitting coil 513 than the element 517. Theelement 519 corresponds to the element 319 of FIG. 10. The element 519is constituted, for example, by a reactance element such as an inductor(reactor, coil) or a capacitor, or a plurality of elements of acombination of such elements.

When the circuit equation of FIG. 14 is set up, Formula (61) isestablished.

$\begin{matrix}{\begin{bmatrix}\begin{matrix}{{j\;\omega\; L_{1}} + {jZ}_{{S\; 1i} - 2} +} \\{j\;\frac{Z_{S\; 1i}Z_{P\; 1i}}{Z_{S\; 1i} + Z_{P\; 1i}}}\end{matrix} & {j\;\omega\; k\sqrt{L_{1}L_{2}}} \\{j\;\omega\; k\sqrt{L_{1}L_{2}}} & {{j\;\omega\; L_{2}} + \frac{{jZ}_{P\; 2i}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)}{Z_{2r} + {jZ}_{S\; 2i} + {jZ}_{P\; 2i}}}\end{bmatrix}{\quad{\begin{bmatrix}I_{1} \\I_{2\;}\end{bmatrix} = \begin{bmatrix}{\frac{Z_{p\; 1i}}{Z_{S\; 1i} + Z_{p\; 1i}}V_{S}} \\0\end{bmatrix}}}} & {{Formula}\mspace{14mu}(61)}\end{matrix}$

When Formula (52) is established, the result of determining theimpedance Z_(1C) (impedance which includes the element 519) of thepower-receiving side seen from the element 519 is determined to a valuerepresented by Formula (62), and this formula does not contain thecoupling coefficient k.

$\begin{matrix}{Z_{1c} = {{K_{I}^{2}\frac{L_{1}}{L_{2}}\left( \frac{{jZ}_{P\; 2i}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)}{Z_{2r} + {jZ}_{S\; 2i} + {jZ}_{P\; 2i}} \right)^{*}} + {j\;\omega\;{L_{1}\left( {1 - K_{I}^{2}} \right)}} + {jZ}_{{S\; 1i} - 2}}} & {{Formula}\mspace{14mu}(62)}\end{matrix}$

Here, when the impedance value of the element 519 is determined so thatFormula (63) is established, the impedance Z_(1C) is represented byFormula (64). Meanwhile, in order to prevent the impedance of theelement 519 from being 0, the coefficient K_(I) is set to a value largerthan 0 and smaller than 1, or a value larger than 1.

$\begin{matrix}{Z_{{S\; 1i} - 2} = {{- \omega}\;{L_{1}\left( {1 - K_{I}^{2}} \right)}}} & {{Formula}\mspace{14mu}(63)} \\{Z_{1c} = {K_{I}^{2}\frac{L_{1}}{L_{2}}\left( \frac{{jZ}_{P\; 2i}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)}{Z_{2r} + {jZ}_{S\; 2i} + {jZ}_{P\; 2i}} \right)^{*}}} & {{Formul}\; a\mspace{14mu}(64)}\end{matrix}$

Then, the result of determining the impedance Z₁ (impedance whichincludes the element 517) of the power-receiving side seen from theelement 517 is determined to a value represented by Formula (65), andthis formula does not contain the coupling coefficient k.

$\begin{matrix}{Z_{1} = {K_{I}^{2}\frac{L_{1}}{L_{2}}\frac{Z_{P\; 1i}{Z_{P\; 2i}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)}^{*}}{{\left( {Z_{P\; 1i} - {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{P\; 2i}}} \right)\left( {{jZ}_{2r} + Z_{S\; 2i}} \right)} + {Z_{P\; 1i}Z_{P\; 2i}}}}} & {{Formul}\; a\mspace{14mu}(65)}\end{matrix}$

When the impedance values of the element 517 and the element 527 aredetermined so that Formula (66) is established, Formula (67) isestablished from Formula (65) and Formula (66).

$\begin{matrix}{Z_{P\; 1i} = {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{P\; 2i}}} & {{Formul}\; a\mspace{14mu}(66)} \\{Z_{1} = {K_{I}^{2}\frac{L_{1}}{L_{2}}\left( {Z_{2r} + {jZ}_{S\; 2i}} \right)^{*}}} & {{Formul}\; a\mspace{14mu}(67)}\end{matrix}$

Thus, the impedance Z_(S) (impedance which does not include the powersource 511) of the power-receiving side seen from the power source 511is determined to a value represented by Formula (68).

$\begin{matrix}{Z_{S} = {K_{I}^{2}\frac{L_{1}}{L_{2}}\left( {Z_{2r} + {j\left( {{\frac{1}{K_{I}^{2}}\frac{L_{2}}{L_{1}}Z_{S\; 1i}} - Z_{S\; 2i}} \right)}} \right)}} & {{Formula}\mspace{14mu}(68)}\end{matrix}$

From Formula (68), the impedance Z_(S) of the power-receiving side seenfrom the power source 511 is independent of the coupling coefficient k.In addition, the real part of the impedance Z_(S) is represented only bythe impedance of the load 525, the self-inductances of thepower-transmitting coil 513 and the power-receiving coil 521 and thecoefficient K_(I), and is not influenced by the impedances of theelements 515, 517, 519, 523 and 527.

Further, in Formula (68), when the imaginary impedance Z_(S1i) satisfiesFormula (69), the imaginary part of Formula (68) is canceled, and theimpedance Z_(S) has only a real part as in Formula (70). In this case,the power factor of the power source 511 is 100%. On the other hand, thevalue of the imaginary impedance Z_(S1i) is shifted from the value ofFormula (69), and thus the power factor can be determined to a desiredvalue without the impedance Z_(S) depending on the coupling coefficientk.

$\begin{matrix}{Z_{S\; 1i} = {K_{I}^{2}\frac{L_{1}}{L_{2\;}}Z_{S\; 2i}}} & {{Formula}\mspace{14mu}(69)} \\{Z_{S} = {K_{I}^{2}\frac{L_{1}}{L_{2\;}}Z_{2r}}} & {{Formula}\mspace{14mu}(70)}\end{matrix}$

Meanwhile, in the circuit configuration of FIG. 10, when the impedancevalues of the element 319 and the element 329 are determined so thatFormula (71) is established, it is possible to derive formulas similarto the above-described formulas.

$\begin{matrix}{Z_{{S\; 1i} - 2} = {{{- \omega}\;{L_{1}\left( {1 - K_{I}^{2}} \right)}} + {K_{I}^{2}\frac{L_{1}}{L_{2\;}}Z_{{S\; 2i} - 2}}}} & {{Formula}\mspace{14mu}(71)}\end{matrix}$

Formula (52) is rearranged to the following Formula (72).

$\begin{matrix}{{\frac{{\omega^{2}\left( {k/K_{I}} \right)}^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{\;{S\; 2i}}} \right)^{2}} = {\frac{\omega^{2}k_{a}^{2}L_{2}^{2}}{Z_{2r}^{2} + \left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)^{2}} = 1}}\left( {k_{a} = {k/K_{I}}} \right)} & {{Formula}\mspace{14mu}(72)}\end{matrix}$

Formula (72) is different from Formula (13) only in a point where theactual coupling coefficient k is changed to an apparent couplingcoefficient k_(a). Accordingly, the aforementioned designing method andcontrol method of a wireless power supply system based on Formula (12)can be applied to designing method and control method of a wirelesspower supply system based on Formula (52).

Subsequently, reference will be made to the circuit configurations ofFIG. 1 and FIG. 4 to describe change in the current I₂ flowing throughthe power-receiving coil when the coefficient K_(I) is other than 1compared with a case when the coefficient K_(I) is 1.

When the coefficient K_(I) is 1, in the circuit configuration of FIG. 1,Formula (73) is established from Formula (11) and Formula (12).

$\begin{matrix}{{\frac{j\;\omega\; L_{2}}{Z_{2r} + {j\left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)}}} = \frac{1}{k}} & {{Formula}\mspace{14mu}(73)}\end{matrix}$

The left side of Formula (73) is equivalent to a response magnificationQ(ω) of a circuit constituted by the power receiver 103 and the load125. The response magnification Q(ω) becomes a resonance magnificationQ_(C)(ω_(C)L₂/Z_(2r)) at a resonance frequency ω_(C)(=−Z_(S2i)/L₂) ofthis circuit. When Q(ω₀) at a frequency (ω₀) which satisfies Formula(73) becomes larger, Q_(C) also becomes larger proportionally to Q(ω₀).Accordingly, the establishment of Formula (12) (or Formula (73)) meansthat the relation of Formula (74) is also established.

$\begin{matrix}{Q_{C} \propto \frac{1}{k}} & {{Formula}\mspace{14mu}(74)}\end{matrix}$

That is, when Formula (12) is established and the coupling coefficient kbecomes smaller, the resonance magnification Q_(C) becomes larger.

Here, the response magnification in the circuit configuration of FIG. 4will be described. The response magnification Q(ω) of FIG. 4 isrepresented by Formula (75).

$\begin{matrix}{{Q(\omega)} = {\frac{j\;\omega\; L_{2}}{\begin{matrix}{{\frac{Z_{P\; 2i}^{2}}{Z_{2r}^{2} + \left( {Z_{S\; 2i} + Z_{P\; 2i}} \right)^{2}}Z_{2r}} +} \\{j\left( {{\omega\; L_{2}} + \frac{Z_{P\; 2i}\left( {Z_{2r}^{2} + {Z_{S\; 2i}\left( {Z_{S\; 2i} + Z_{P\; 2i}} \right)}} \right)}{Z_{2r}^{2} + \left( {Z_{S\; 2i} + Z_{P\; 2i}} \right)^{2}}} \right)}\end{matrix}}}} & {{Formula}\mspace{14mu}(75)}\end{matrix}$

Since the resonance magnification Q_(C) is a case when an imaginary partof a denominator of Formula (75) is 0, the resonance magnification Q_(C)is represented by Formula (76).

$\begin{matrix}{Q_{C} = {\frac{Z_{2r}^{2} + \left( {Z_{S\; 2i} + Z_{P\; 2i}} \right)^{2}}{Z_{P2i}^{2}}\frac{\omega_{C}L_{2}}{Z_{2r}}}} & {{Formula}\mspace{14mu}(76)}\end{matrix}$

Here, the ratio of the current I₂ flowing through the power-receivingcoil 221 to the current I_(L) flowing through the load 225 isrepresented by Formula (77).

$\begin{matrix}{\frac{I_{2}}{I_{L}} = \frac{Z_{2r} + {j\left( {Z_{S\; 2i} + Z_{P\; 2i}} \right)}}{{jZ}_{P\; 2i}}} & {{Formula}\mspace{14mu}(77)}\end{matrix}$

Formula (76) becomes Formula (78) from Formula (77).

$\begin{matrix}{Q_{C} = {{\frac{I_{2}}{I_{L}}}^{2}\frac{\omega_{C}L_{2}}{Z_{2r}}}} & {{Formula}\mspace{14mu}(78)}\end{matrix}$

The relation of Formula (79) is established from Formula (74) andFormula (78).

$\begin{matrix}{{{\frac{I_{2}}{I_{L}}}^{2}\frac{\omega_{C}L_{2}}{Z_{2r}}} \propto \frac{1}{k}} & {{Formula}\mspace{14mu}(79)}\end{matrix}$

Formula (79) shows that the current I₂ flowing through thepower-receiving coil 221 becomes larger as the coupling coefficient kbecomes smaller.

Hereinabove a case in which the coefficient K_(I) is 1 (that is, Formula(12) is established) has been described. Hereunder, change in thecurrent I₂ flowing through the power-receiving coil when the coefficientK_(I) is other than 1 will be described. When Formula (51) isestablished, Formula (80) is established rather than Formula (73).

$\begin{matrix}{{\frac{j\;\omega\; L_{2}}{Z_{2r} + {j\left( {{\omega\; L_{2}} + Z_{S\; 2i}} \right)}}} = \frac{K_{I}}{k}} & {{Formula}\mspace{14mu}(80)}\end{matrix}$

Similar to the derivation of Formula (79), when Formula (51) isestablished, the relation of Formula (81) is established.

$\begin{matrix}{{{\frac{I_{2}}{I_{L}}}^{2}\frac{\omega_{C}L_{2}}{Z_{2r}}} \propto \frac{K_{I}}{k}} & {{Formula}\mspace{14mu}(81)}\end{matrix}$

When constant electric power is supplied to the load 225, by setting therange of the coefficient K_(I) to 0<K_(I)<1, it is possible to reducethe current I₂ flowing through the power-receiving coil 221 comparedwith a case where Formula (12) is established.

When the wireless power supply system is applied to a charging system ofan electric vehicle, for example, the power receiver is mounted on theelectric vehicle. In this case, it may be desired to reduce the size ofthe power receiver since the installation location of the power receiveron the electric vehicle is limited. In order to reduce the size of thepower receiver, the conducting wire forming the power-receiving coil maybe made thinner, for example. When making the conducting wire thinner,the electric resistance of the conducting wire increases, and thus thecalorific value increases. Accordingly, as shown in Formula (73), bysetting the range of the coefficient K_(I) to 0<K_(I)<1, it is possibleto reduce the current I₂ compared with a case where Formula (12) isestablished, and thus it is possible to reduce the calorific value.

Meanwhile, in the same manner as is described above, when it is desiredto reduce the current I₁ flowing through the power-transmitting coil213, the range of the coefficient K_(I) is set so as to satisfy 1<K_(I).

In the embodiments and the modification examples, the wireless powersupply system including the power transmitter and the power receiver isdescribed. However, the present disclosure is not limited to such aconfiguration, and the present disclosure may be applied to a powerreceiver that receives electric power wirelessly from a powertransmitter including a power-transmitting coil to which AC power of afrequency is input from a power source. This power receiver includes thesame configuration as that of the power receiver 103, 203 or 303described in the embodiments and the modification examples. That is, thepower receiver of the present disclosure includes a power-receiving coilmagnetically coupled to the power-transmitting coil at a couplingcoefficient, and a power-receiving-side series element (firstpower-receiving-side series element) which is coupled in series to thepower-receiving coil and which has imaginary impedance jZ_(S2i). Thepower-receiving coil may have the same configuration as that of thepower-receiving coil 121, 221 or 321, and the power-receiving-sideseries element may have the same configuration as that of the element123, 223 or 323. In the power receiver of the present disclosure, thefrequency of AC power which is output by the power source and theimaginary impedance of the power-receiving-side series element may bedetermined so that the impedance of the power-receiving side seen fromthe power source is independent of the coupling coefficient k when thecoupling coefficient k changes. In other words, the power receiver ofthe present disclosure may be configured to regulate at least one of thefrequency of the AC power which is output by the power source and theimaginary impedance of the power-receiving-side series element so thatthe impedance of the power-receiving side seen from the power source isindependent of the coupling coefficient k when the coupling coefficientk changes. The power receiver may instruct the power source to change afrequency through a communication portion or the like.

INDUSTRIAL APPLICABILITY

According to the present disclosure, it is possible to provide awireless power supply system and a power receiver which are capable ofsuppressing a fluctuation in impedance of a power-receiving side seenfrom a power source, when a coupling coefficient changes.

What is claimed is:
 1. A wireless power supply system comprising: apower transmitter; and a power receiver, the power transmittercomprising a power-transmitting coil to which AC power of a frequency isinput from a power source, and the power receiver comprising: apower-receiving coil magnetically coupled to the power-transmitting coilat a coupling coefficient; and a first power-receiving-side serieselement coupled in series to the power-receiving coil and havingimaginary impedance jZ_(S2i), wherein the frequency, the couplingcoefficient and the imaginary impedance are determined on the basis ofsatisfying the following formula, $\begin{matrix}{{\frac{I_{2}}{I_{1}}} = {K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(1)}\end{matrix}$ where L₁ is self-inductance of the power-transmittingcoil, L₂ is self-inductance of the power-receiving coil, I₁ is a currentflowing through the power-transmitting coil, I₂ is a current flowingthrough the power-receiving coil, and K_(I) is a coefficient.
 2. Thewireless power supply system according to claim 1, wherein thecoefficient K_(I) is a value larger than 0 and smaller than 1, or avalue larger than
 1. 3. The wireless power supply system according toclaim 2, wherein: the power transmitter further comprises: apower-transmission-side parallel element coupled in parallel to thepower-transmitting coil and having imaginary impedance jZ_(P1i); and afirst power-transmission-side series element coupled in series to thepower-transmitting coil at a position closer to the power-transmittingcoil than the power-transmission-side parallel element and havingimaginary impedance jZ_(S1i-2); the power receiver further comprises apower-receiving-side parallel element coupled in parallel to thepower-receiving coil at a position closer to the power-receiving coilthan the first power-receiving-side series element and having imaginaryimpedance jZ_(P2i); the imaginary impedance of the firstpower-transmission-side series element satisfies the following formula;andZ _(S1i-2) =−ωL ₁(1−K _(I) ²)  Formula (2) the imaginary impedances ofthe power-transmission-side parallel element and thepower-receiving-side parallel element satisfy the following formula.$\begin{matrix}{Z_{P\; 1i} = {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{P\; 2i}}} & {{Formula}\mspace{14mu}(3)}\end{matrix}$
 4. The wireless power supply system according to claim 3,wherein: a variable range of the frequency is determined; a fluctuationrange of the coupling coefficient is determined; and the imaginaryimpedances of the first power-receiving-side series element and thepower-receiving-side parallel element are determined so as to satisfyFormula (1), when the frequency is an upper limit or a lower limit ofthe variable range and the coupling coefficient is an upper limit or alower limit of the fluctuation range.
 5. The wireless power supplysystem according to claim 4, wherein the imaginary impedances of thefirst power-receiving-side series element and the power-receiving-sideparallel element are determined so that a phase difference between anelectromotive force induced in the power-receiving coil by magneticcoupling of the power-transmitting coil to the power-receiving coil andthe current of the power receiving coil is 0°.
 6. The wireless powersupply system according to claim 4, wherein: a load whose impedancefluctuates is coupled to the power receiver; and the imaginaryimpedances of the first power-receiving-side series element and thepower-receiving-side parallel element are determined so as to satisfyFormula (1) irrespective of the impedance of the load, when thefrequency is the upper limit or the lower limit of the variable rangeand the coupling coefficient is the lower limit of the fluctuationrange.
 7. The wireless power supply system according to claim 3, whereinthe first power-receiving-side series element is an inductor, and thepower-receiving-side parallel element is a capacitor.
 8. The wirelesspower supply system according to claim 3, wherein the firstpower-receiving-side series element and the power-receiving-sideparallel element are capacitors.
 9. The wireless power supply systemaccording to claim 2, wherein: the power transmitter further comprises:a power-transmission-side parallel element coupled in parallel to thepower-transmitting coil and having imaginary impedance jZ_(P1i); and afirst power-transmission-side series element coupled in series to thepower-transmitting coil at a position closer to the power-transmittingcoil than the power-transmission-side parallel element and havingimaginary impedance jZ_(S1i-2); the power receiver further comprises: apower-receiving-side parallel element coupled in parallel to thepower-receiving coil at a position closer to the power-receiving coilthan the first power-receiving-side series element and having imaginaryimpedance jZ_(P2i); and a second power-receiving-side series elementcoupled in series to the power-receiving coil at a position closer tothe power-receiving coil than the power-receiving-side parallel elementand having imaginary impedance jZ_(S2i-2); the imaginary impedances ofthe first power-transmission-side series element and the secondpower-receiving-side series element satisfy the following formula; and$\begin{matrix}{Z_{{S1i} - 2} = {{{- \omega}\;{L_{1}\left( {1 - K_{I}^{2}} \right)}} + {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{{S\; 2i} - 2}}}} & {{Formula}\mspace{14mu}(4)}\end{matrix}$ the imaginary impedances of the power-transmission-sideparallel element and the power-receiving-side parallel element satisfythe following formula. $\begin{matrix}{Z_{P\; 1i} = {K_{I}^{2}\frac{L_{1}}{L_{2\;}}Z_{P\; 2i}}} & {{Formula}\mspace{14mu}(5)}\end{matrix}$
 10. The wireless power supply system according to claim 9,wherein: a variable range of the frequency is determined; a fluctuationrange of the coupling coefficient is determined; and the imaginaryimpedances of the first power-receiving-side series element, the secondpower-receiving-side series element and the power-receiving-sideparallel element are determined so as to satisfy Formula (1), when thefrequency is an upper limit or a lower limit of the variable range andthe coupling coefficient is an upper limit or a lower limit of thefluctuation range.
 11. The wireless power supply system according toclaim 10, wherein: a load whose impedance fluctuates is coupled to thepower receiver; and the imaginary impedances of the firstpower-receiving-side series element, the second power-receiving-sideseries element and the power-receiving-side parallel element aredetermined so as to satisfy Formula (1) irrespective of the impedance ofthe load, when the frequency is the upper limit or the lower limit ofthe variable range and the coupling coefficient is the lower limit ofthe fluctuation range.
 12. The wireless power supply system according toclaim 10, wherein the imaginary impedances of the firstpower-receiving-side series element, the second power-receiving-sideseries element and the power-receiving-side parallel element aredetermined so that a phase difference between an electromotive forceinduced in the power-receiving coil by magnetic coupling of thepower-transmitting coil to the power-receiving coil and the current ofthe power receiving coil is 0°.
 13. The wireless power supply systemaccording to claim 9, wherein the first power-receiving-side serieselement is an inductor, and the second power-receiving-side serieselement and the power-receiving-side parallel element are capacitors.14. The wireless power supply system according to claim 9, wherein thefirst power-receiving-side series element, the secondpower-receiving-side series element and the power-receiving-sideparallel element are capacitors.
 15. The wireless power supply systemaccording to claim 1, wherein: the power transmitter further comprises apower-transmission-side series element coupled in series to thepower-transmitting coil and having imaginary impedance jZ_(s1i); and theimaginary impedances of the power-transmission-side series element andthe first power-receiving-side series element satisfy the followingformula. $\begin{matrix}{Z_{S\; 1i} = {\frac{L_{1}}{L_{2}}\left( {{K_{I}^{2}Z_{S\; 2i}} + {\left( {K_{I}^{2} - 1} \right)\omega\; L_{2}}} \right)}} & {{Formula}\mspace{14mu}(6)}\end{matrix}$
 16. The wireless power supply system according to claim 3,wherein: the power transmitter further comprises apower-transmission-side series element coupled in series to thepower-transmitting coil at a position closer to the power source thanthe power-transmission-side parallel element and having imaginaryimpedance jZ_(S1i); and the imaginary impedances of thepower-transmission-side series element and the firstpower-receiving-side series element satisfy the following formula.$\begin{matrix}{Z_{S\; 1i} = {K_{I\;}^{2}\frac{L_{1}}{L_{2\;}}Z_{S\; 2i}}} & {{Formula}\mspace{14mu}(7)}\end{matrix}$
 17. The wireless power supply system according to claim 9,wherein: the power transmitter further comprises a secondpower-transmission-side series element coupled in series to thepower-transmitting coil at a position closer to the power source thanthe power-transmission-side parallel element and having imaginaryimpedance jZ_(S1i); and the imaginary impedances of the secondpower-transmission-side series element and the firstpower-receiving-side series element satisfy the following formula.$\begin{matrix}{Z_{S\; 1i} = {K_{I}^{2}\frac{L_{1}}{L_{2}}Z_{S\; 2i}}} & {{Formula}\mspace{14mu}(8)}\end{matrix}$
 18. The wireless power supply system according to claim 2,wherein: a fluctuation range of the coupling coefficient is determined;and the coefficient K_(I) satisfies 0<K_(I)<1.
 19. The wireless powersupply system according to claim 1, wherein: a fluctuation range of thecoupling coefficient is determined; and when the self-inductances of thepower-transmitting coil and the power-receiving coil change on the basisof change in the coupling coefficient, the self-inductances of thepower-transmitting coil and the power-receiving coil take values withina changing range of the self-inductances depending on change in thecoupling coefficient within the fluctuation range.
 20. A power receiverthat receives electric power wirelessly from a power transmittercomprising a power-transmitting coil to which AC power of a frequency isinput from a power source, the power receiver comprising: apower-receiving coil magnetically coupled to the power-transmitting coilat a coupling coefficient; and a first power-receiving-side serieselement coupled in series to the power-receiving coil and havingimaginary impedance jZ_(S2i), wherein the frequency, the couplingcoefficient and the imaginary impedance are determined on the basis ofsatisfying the following formula, $\begin{matrix}{{\frac{I_{2}}{I_{1\;}}} = {K_{I}\sqrt{\frac{L_{1}}{L_{2}}}}} & {{Formula}\mspace{14mu}(9)}\end{matrix}$ where L₁ is self-inductance of the power-transmittingcoil, L₂ is self-inductance of the power-receiving coil, I₁ is a currentflowing through the power-transmitting coil, I₂ is a current flowingthrough the power-receiving coil, and K_(I) is a coefficient.